CN103698003A - PSD (power spectral density) algorithm-based low-power-consumption real-time vibration monitoring system and method - Google Patents

PSD (power spectral density) algorithm-based low-power-consumption real-time vibration monitoring system and method Download PDF

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CN103698003A
CN103698003A CN201310689446.5A CN201310689446A CN103698003A CN 103698003 A CN103698003 A CN 103698003A CN 201310689446 A CN201310689446 A CN 201310689446A CN 103698003 A CN103698003 A CN 103698003A
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data
psd
module
acceleration
power
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丁德宝
季锦章
沈庆宏
戴鹏飞
陈红梅
丁华平
张勇
都思丹
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NANJING GENTURE ELECTRONIC INFORMATION Co Ltd
Nanjing University
Jiangsu Provincial Communication Planning and Design Institute Co Ltd
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NANJING GENTURE ELECTRONIC INFORMATION Co Ltd
Nanjing University
Jiangsu Provincial Communication Planning and Design Institute Co Ltd
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Abstract

The invention discloses a PSD (power spectral density) algorithm-based low-power-consumption real-time vibration monitoring system applied to health monitoring of a major infrastructure construction structure. The system comprises a sensing acquisition module, a data processing module, a data communication module and a power supply module. The system works at a key point of the infrastructure construction structure, wherein the sensing acquisition module acquires the vibration information of the key point of the structure and obtains three-dimensional vibration acceleration data of the key point of the structure; after the data processing module performs certain pre-processing on the acquired data, the pre-processed data are transmitted to gateway equipment through the data communication module, so that structural vibration data are provided for the health monitoring of the infrastructure construction structure. According to the system and the method, through PSD algorithm transplant and a low noise design, the energy consumption of the system is reduced, the service life of the system is prolonged, the anti-jamming capability of the system is improved, and the method and the system can adapt to complex and demanding monitoring environments.

Description

The real-time vibration monitor system of a kind of low-power consumption based on PSD algorithm and method
Technical field
The present invention relates to emergency monitoring and the forewarn technology of infrastructure architecture safe condition, be specifically related to a kind of real-time vibration monitor system of low-power consumption that is applied to great infrastructure architecture health monitoring.
Background technology
The great infrastructure such as bridge, tunnel within the operation phase, will constantly degenerate due to material aging the phase by its structural behaviour, cause its security constantly to reduce; Meanwhile, various disasteies (typhoon, flood, earthquake), man-made disaster (traffic hazard, terrorist activity) and lasting traffic loading also will cause infrastructure architecture to produce all kinds of damages, may produce the unexpected collapse accident of infrastructure, endanger public security, cause country, people life property loss.In addition, infrastructure is being carried out in maintenance processes, in default of the real time data information of facility structure, maintenance processes often cost is very large, but produces little effect.Therefore, by infrastructure architecture situation is monitored in real time, obtain the status information of infrastructure architecture, can send immediately early warning signal during in unsafe condition in infrastructure architecture, thereby take measures in time.When infrastructure is carried out to maintenance, can definitely judge the damage position of infrastructure, degree of impairment, makes the maintenance measure can be more accurate, more effective, not only can improve infrastructure operation security, can also significantly reduce maintenance costs.
At present the most of great infrastructure of China as bridge etc., has all been disposed structural healthy monitoring system, generally all comprises the monitoring to vibration information.Yet, all there are a series of limitation in the vibration monitoring device for infrastructure architecture monitoring system of having implemented at present, one, poor anti jamming capability, infrastructure architecture health monitoring systems is normally operated in complicated external environment, under the impact of various factors, girder construction health monitoring systems is always subject to the interference of noise, a large amount of status informations of structure are submerged among noise, cause damaging discrimination on the low side, make directly by the accurate recognition structure of sampled signal, to damage; Its two, energy supply is limited, lifetime of system is shorter.Monitoring for infrastructure architecture state, often need the data volume of collection huge, in data processing and transmitting procedure, energy consumption is very many, and being limited to monitoring structural health conditions environment, a lot of vibration monitor system often need powered battery, and during infrastructure operation, it is very inconvenient that structural healthy monitoring system is carried out to battery altering, and this just makes the mission life of equipment greatly shorten; Its three, cannot accomplish real-time monitoring.Be limited to energy consumption and stable equipment operation, the vibration monitor system that is applied at present infrastructure architecture health monitoring field cannot be accomplished the real-time monitoring to configuration state.
Therefore, for the great infrastructure architecture health monitoring of complex environment, need a kind of brand-new vibration monitor system, can meet monitoring site low-power consumption, low noise, the requirement of monitoring in real time.
Summary of the invention
The object of the present invention is to provide a kind of vibration real-time monitoring system and method that is applied to great infrastructure architecture health monitoring.The problem existing for aforementioned vibration monitor system, designs a kind of novel vibration real-time monitoring system that is applied to great infrastructure architecture health monitoring.The feature of this system is, low noise, low-power consumption, can realize real-time monitoring, is applicable to the great infrastructure architecture safety monitoring of complex environment.
The object of the present invention is achieved like this, and the real-time vibration monitor system of a kind of low-power consumption based on PSD algorithm, comprises sensing acquisition module, data processing module, data communication module, and power module;
Described sensing acquisition module, carries out data acquisition to the vibration information of infrastructure architecture key point, the three-dimensional acceleration simulation data-signal collecting is processed to the acceleration value of one group of three-dimensional of output;
Described data processing module, the acceleration value of the three-dimensional of exporting in sensing acquisition module is carried out to pre-service, and adopt PSD to calculate data, draw one group of power spectrum degrees of data, again these group data are carried out to data packing, the packet of output one group communication protocol form;
Described data communication module, is sent to the network equipment by data packed in data processing module;
Described power module, presses for whole system provides galvanic current.
Described sensing acquisition module utilizes low noise acceleration transducer to carry out data acquisition to the vibration information of infrastructure architecture key point, and to the three-dimensional acceleration simulation data-signal collecting with the form of voltage amplify, after filtering processes, by the sample frequency of 10-280Hz, carry out A/D conversion again, convert the acceleration value output of three-dimensional to.
Improvement of the present invention is: the three-dimensional acceleration simulation data-signal acquisition method in described sensing acquisition module: adopt three M1221 chips, mutual vertical welding, the acceleration information of X, Y, tri-directions of Z is independently gathered, and by different passages, be sent to acp chip and process, form the Acceleration Acquisition System of a three-dimensional.
It is continuous in described sensing acquisition module, the vibration information of infrastructure architecture key point being carried out to data acquisition; Described sensing acquisition module is accepted the configuration parameter of data processing module, and described parameter comprises sample frequency, filter cutoff frequency.
The power supply of described power module can be one or more the combination in powered battery, solar powered and wind power supply.
Described data communication module adopts ICP/IP protocol and gateway device wired connection to send data, or adopts Zigbee agreement and base station equipment to carry out radio communication transmission data; In described data communication module transmitting procedure, adopt unified data layout, described data layout comprises Data Identification, timestamp, acceleration direction, sensing data territory.
The present invention also provides a kind of method for supervising of the real-time vibration monitor system of low-power consumption based on PSD algorithm, described sensing acquisition module, the vibration information of infrastructure architecture key point is carried out to data acquisition, the three-dimensional acceleration simulation data-signal collecting is processed to the acceleration value of one group of three-dimensional of output; Described data processing module, the acceleration value of the three-dimensional of exporting in sensing acquisition module is carried out to pre-service, and adopt PSD to calculate data, draw one group of power spectrum degrees of data, again these group data are carried out to data packing, the packet of output one group communication protocol form; Described data communication module, is sent to the network equipment by data packed in data processing module; Be arranged on infrastructure architecture key point place, system will be carried out continuous data acquisition to structural vibration information; The three-dimensional acceleration simulation data-signal collecting amplifies, after filtering processes, by the sample frequency of 10-280Hz, carries out A/D conversion with the form of voltage, converts three-dimensional acceleration numerical value to; Three-dimensional acceleration data, after PSD calculates, are obtained the frequency domain information of vibration, obtain the PSD data that efficiency is higher; PSD data are sent to data center and carry out analyzing and processing, can know clearly the vibration fundamental frequency of infrastructure architecture; Can be used for thus calculating strain mode or strain pulling force, to the long term monitoring of infrastructure architecture vibration fundamental frequency, can directly reflect and measure whether structure changes or extremely.
Further, Fourier transform in described data processing module and power spectral density PSD computing method: first data are carried out to error checking and memory allocated space, then according to the parameter of configuration, selector channel and selection window are set, use the frequency spectrum in the power spectrum density computing function calculation window that improved discrete fourier transform algorithm forms and preserve transmission calculating end signal after the data of having calculated all windows and passage.
Further, described data communication module adopts ICP/IP protocol and gateway device wired connection to send data, or adopts Zigbee agreement and base station equipment to carry out radio communication transmission data; And in described data communication module transmitting procedure, adopt unified data layout, described data layout comprises Data Identification, timestamp, acceleration direction, sensing data territory.
Further, described power module provides stable 5V voltage for whole system.
The present invention transplants low noise acceleration transducer in real-time vibration monitor system, improves the antijamming capability of system, solves traditional vibration monitor system noiseproof feature in monitoring structural health conditions practical application poor, damage discrimination problem on the low side.The acceleration transducer using in system be a cheaply, integrated acceleration sensing chip, be applied to the instrument design below intermediate frequency, there is extremely low noise figure.To can reach-2g of the measurement range of acceleration~+ 2g, there is lower temperature sensitivity and thermal gradient, built-in temperature sensor, can carry out Design of Temperature Compensation.Its inner integrated sensor, amplifier and difference output stage, can steady operation at-55~+ 125 ℃.Be applicable to very much the practical application in bridge structural health monitoring field.
Beneficial effect of the present invention:
The present invention transplants PSD algorithm in data processing module, the energy consumption while greatly reducing system works.The basic frequency domain information that Fourier transform and power spectrum density (PSD) function is comprising signal, and the performance of power system.And work as sample frequency, set one regularly with other users, the data volume constant (with size and the time-independent of image data amount) after processing.So, when system requirements does not need spatial information, utilize data processing module to process the data that raw data obtains only comprising frequency domain characteristic and send it back data packet number and the time that data center can reduce transmission greatly.And be all at data communication module by most of energy consumption of the known vibration monitor system of contrast experiment, data communication module consumes more electric energy while carrying out calculating than data processing module when transmission data.Therefore,, by adopting PSD algorithm to carry out pre-service to raw data, can, the in the situation that of lost data validity not, greatly reduce system energy consumption.
In the present invention, the real-time vibration monitor system of low-power consumption can realize 24 hours round-the-clock Real-time Collections to the monitoring of infrastructure architecture key point, in real time monitoring.Each second status information of the structure of infrastructure all can be collected, process, and finally delivers to data center and analyze, to tackle the various emergency case during infrastructure operation.
The present invention, by the collection of infrastructure architecture key point vibration information, processing, transmission, makes infrastructure administrative authority obtain infrastructure real-time status information, supports, for emergent decision-making provides Data support for infrastructure maintenance, maintenance provide science.
The present invention transplants by PSD low-power consumption algorithm, reduces the whole energy consumption of supervisory system, extends lifetime of system, saves monitoring spending.
The present invention, by Low Noise Design, increases system rejection to disturbance ability, improves data accuracy, validity.The damage discrimination that raising is surveyed infrastructure architecture, improves the efficiency of maintenance, maintenance.
The present invention realizes real-time monitoring, not only greatly improves data validity, also makes system can tackle the various emergency case such as nature, man-made disaster.Crisis is processed evidence-based.
The present invention relies on advanced test macro, reduces labour, in infrastructure maintenance, maintenance processes, reduces the error that human factor causes.
The real-time vibration monitor system of low noise that is applied to great infrastructure architecture health field of the present invention, has its inherent advantage.Adopt Low Noise Design, improve data accuracy, increase damage discrimination.Adopt low-power consumption algorithm to transplant, reduce system power dissipation, extend system serviceable life.It is feature of monitoring in real time, can successfully manage various urgent emergency case during infrastructure operation.These many advantages, make system can adapt to complexity, severe, various infrastructure architecture health monitoring environment.
Accompanying drawing explanation
Fig. 1 is entire system block architecture diagram of the present invention;
Fig. 2 is working-flow figure;
Fig. 3 is sensing acquisition modular circuit theory diagram;
Fig. 4 is entire system schematic block circuit diagram;
Fig. 5 is data processing module software flow pattern;
Fig. 6 is PSD algorithm flow chart.
Specific embodiments
Below in conjunction with accompanying drawing and instantiation, the present invention is elaborated, but native system range of application is not limited to this example.
In conjunction with Fig. 1, system comprises sensing acquisition module, data processing module, data communication module, and power module described in this example.Sensing acquisition module is responsible for infrastructure vibration information to carry out data acquisition, and to the three-dimensional acceleration simulation data-signal collecting amplify, filtering, the processing such as A/D conversion, export the acceleration value of one group of three-dimensional.In addition, sensing acquisition module can be accepted the configuration parameter of data processing module, and the monitoring requirement according to different, is configured parameters such as sample frequency, filter cutoff frequencies.Data processing module is accepted the acceleration information from sensing acquisition module, it is carried out after certain pre-service, carry out PSD calculating, calculate one group of power spectrum degrees of data, and these group data are carried out to data packing by set communication protocol, its output is the packet of a group communication protocol form.Data communication module takes out packed packet from internal memory, by ICP/IP protocol or Zigbee agreement, carries out data transmission.Its communication mode can, according to actual monitoring needs, be selected.In its transmitting procedure, adopt unified data layout, comprise Data Identification, timestamp, acceleration direction and sensing data territory, irrelevant with the data transmission adopting.Power module provides stable 5V voltage for whole system, and its power supply can be powered battery, solar powered, powered by wind energy, or a few person is complementary, and power supply mode can be selected according to field monitoring environment.
In conjunction with Fig. 2, this example is arranged on to infrastructure architecture key point place, system will be carried out continuous data acquisition to structural vibration information.The three-dimensional acceleration simulation data-signal collecting amplifies, after filtering etc. processes, by certain sample frequency, carries out A/D conversion with the form of voltage, converts three-dimensional acceleration numerical value to.Three-dimensional acceleration data, after PSD calculates, are obtained the frequency domain information of vibration, obtain the PSD data that efficiency is higher.PSD data are sent to data center and carry out analyzing and processing, can know clearly the vibration fundamental frequency of infrastructure architecture.Can be used for thus calculating strain mode or strain pulling force, to the long term monitoring of infrastructure architecture vibration fundamental frequency, can directly reflect and measure whether structure changes or extremely.
In conjunction with Fig. 3, the acp chip QF4A512 that described sensing acquisition module adopts is 4 passage programmable signal conversion chips of Quickfliter company design, chip itself is integrated amplification, anti-aliasing filter, analog to digital conversion and processing unit.Can carry out digital-to-analog conversion and the 512 rank high precision FIR filtering of maximum 16 word lengths to input simulating signal.Support the simulating signal input that 4 tunnels are separate.Its sampling word length, filter parameter etc. can arrange by internal register.The digital signal that simulating signal obtains through QF4A512 sampling processing.Sensor chip adopts the M1221 low noise acceleration chip of SILICON DESIGNS company design, and M1221 chip is transplanted in the front end of QF4A512 chip.Monitoring to infrastructure architecture vibration information, will gather the acceleration information of three-dimensional conventionally, so native system adopts three M1221 chips, mutually vertical welding.The acceleration information of X, Y, tri-directions of Z is independently gathered, and by different passages, is sent to QF4A512 chip and processes, and forms a three-dimensional Acceleration Acquisition System.Sensor chip rear class has designed a differential amplifier circuit, to suppress temperature noise.QF4A512 chip carries out exchanges data by SPI interface and external processor.
In conjunction with Fig. 4, in example, data processing module comprises processor and reservoir, and native system is supported many architecture processors such as ARM, imote2, AVR.Data processing module is connected by bus with sensing acquisition module, carries out exchanges data.Meanwhile, data processing module provides 3.3V normal voltage for sensing acquisition module.System power supply module comprises externally fed structure and mu balanced circuit.According to monitoring field actual environment, can select the various ways such as powered battery, wind-power electricity generation, sun power, or various ways is complementary.Mu balanced circuit provides 5V normal voltage for whole system.Data communication module has two kinds of configurations available, and both configurable ICP/IP protocol was carried out ethernet communication, and also configurable radio frequency chip CC2420, carries out radio communication by Zigbee agreement.
In conjunction with Fig. 5, for guaranteeing the real-time monitoring to structural vibration information, during Software for Design, adopt multi-thread programming, by the mode of shared drive object, carry out inter-thread communication, the data of guaranteeing each second all collected, send, process.When exchanges data is carried out in data communication module and outside, if mechanical disorder occurs data receiver, system is by data buffer storage in local storage, and pending data take over party computing machine is uploaded after recovering again.Even if can guarantee that like this data center breaks down, monitor data can not lost yet.
In conjunction with Fig. 6, when vibration monitor system operation in real time, the energy consumption of data communication module accounts for the major part of system total energy consumption.If system power supply voltage is U n, electric current is I n, transmitting time is t ns, data communication module power consumption is
W n=U n×I n×t ns (1)
Because node frequency acquisition is generally greater than 50Hz, and the collection of structural vibration information is comprised to three-dimensional, during Real-Time Monitoring, data volume is huge, when data transmission rate and host-host protocol are fixedly time, and t nswith the proportional relation of data volume sending.So work as U nand I nall fixedly time, reduce sending data volume and reduce and send data time and can reduce node power consumption.
Suppose that the original data sequence collecting is X (t), its autocorrelation function is R (t), R (t) is carried out to Fourier's variation and obtain:
u ( v ) = ∫ - ∞ ∞ R ( t ) e - i 2 πtv dt - - - ( 2 )
Between u (v) and R (t), meet Parserval formula:
∫ - ∞ ∞ R 2 ( t ) dt = ∫ - ∞ ∞ | u ( v ) | 2 dv - - - ( 3 )
By adopting tail function
R T(t)=R(t),|t|≤T (4)
To R (t) intercepting, meet equally Parserval formula.
To Parserval formula both sides integration, can obtain power spectral density function.
P ( v ) = Lim T → ∞ | u r ( v ) 2 | 2 T - - - ( 5 )
When actual computation, to finite length sequence, adopt Welch method to carry out segmentation by the window of certain length, obtain periodogram, then average, therefore resulting power spectrum density sequence length is only relevant with the length of window of setting.If system adopts 100HZ sampling rate, resulting raw data per second has N1=100*60*30=18000, and concerning Real-time Collection, the data that obtain after certain hour are magnanimity, in data communication process, have consumed a large amount of energy.
And the data sequence length obtaining by PSD algorithm is determined by window size, irrelevant with acquisition time.According to generally, if set window size, be that 1024, PSD sequence length is N2=512.With respect to raw data, data volume is reduced greatly.
The raw acceleration data collecting is carried out to PSD calculating, can, in the situation that not affecting data validity, significantly reduce the data volume that needs transmission, to reach the object of low-power consumption.
When carrying out PSD calculating, first carry out error checking and memory allocated space, then according to the parameter of configuration, selector channel and selection window are set, use the frequency spectrum in the power spectrum density computing function calculation window that improved discrete fourier transform algorithm forms and preserve transmission calculating end signal after the data of having calculated all windows and passage.
This example is transplanted by PSD algorithm, adopts Low Noise Design, mainly completes the vibration information monitoring piling up in infrastructure architecture health monitoring application.In application, mount the system to infrastructure architecture key point place, structural vibration information is carried out to data acquisition, pre-service, storage, communication, for infrastructure architecture health monitoring provides reliable vibration data.The design of system meets complicated, severe field monitoring environment, and can adapt to the monitoring field of various features.

Claims (10)

1. the real-time vibration monitor system of the low-power consumption based on PSD algorithm, is characterized in that: comprise sensing acquisition module, data processing module, data communication module, and power module;
Described sensing acquisition module, carries out data acquisition to the vibration information of infrastructure architecture key point, the three-dimensional acceleration simulation data-signal collecting is processed to the acceleration value of one group of three-dimensional of output;
Described data processing module, the acceleration value of the three-dimensional of exporting in sensing acquisition module is carried out to pre-service, and adopt PSD to calculate data, draw one group of power spectrum degrees of data, again these group data are carried out to data packing, the packet of output one group communication protocol form;
Described data communication module, is sent to the network equipment by data packed in data processing module;
Described power module, presses for whole system provides galvanic current.
2. the real-time vibration monitor system of the low-power consumption based on PSD algorithm according to claim 1, it is characterized in that: described sensing acquisition module utilizes low noise acceleration transducer to carry out data acquisition to the vibration information of infrastructure architecture key point, and to the three-dimensional acceleration simulation data-signal collecting with the form of voltage amplify, after filtering processes, by the sample frequency of 10-280Hz, carry out A/D conversion again, convert the acceleration value output of three-dimensional to.
3. the real-time vibration monitor system of the low-power consumption based on PSD algorithm according to claim 1 and 2, it is characterized in that: the three-dimensional acceleration simulation data-signal acquisition method in described sensing acquisition module: adopt three M1221 chips, mutual vertical welding, the acceleration information of X, Y, tri-directions of Z is independently gathered, and by different passages, be sent to acp chip and process, form the Acceleration Acquisition System of a three-dimensional.
4. the real-time vibration monitor system of the low-power consumption based on PSD algorithm according to claim 1 and 2, is characterized in that: it is continuous in described sensing acquisition module, the vibration information of infrastructure architecture key point being carried out to data acquisition; Described sensing acquisition module is accepted the configuration parameter of data processing module, and described parameter comprises sample frequency, filter cutoff frequency.
5. the real-time vibration monitor system of the low-power consumption based on PSD algorithm according to claim 1 and 2, is characterized in that: the power supply of described power module can be one or more the combination in powered battery, solar powered and wind power supply.
6. the real-time vibration monitor system of the low-power consumption based on PSD algorithm according to claim 1, it is characterized in that: described data communication module adopts ICP/IP protocol and gateway device wired connection to send data, or adopt Zigbee agreement and base station equipment to carry out radio communication transmission data; In described data communication module transmitting procedure, adopt unified data layout, described data layout comprises Data Identification, timestamp, acceleration direction, sensing data territory.
7. according to the method for supervising of the real-time vibration monitor system of low-power consumption based on PSD algorithm one of claim 1 to 6 Suo Shu, it is characterized in that: described sensing acquisition module, the vibration information of infrastructure architecture key point is carried out to data acquisition, the three-dimensional acceleration simulation data-signal collecting is processed to the acceleration value of one group of three-dimensional of output; Described data processing module, the acceleration value of the three-dimensional of exporting in sensing acquisition module is carried out to pre-service, and adopt PSD to calculate data, draw one group of power spectrum degrees of data, again these group data are carried out to data packing, the packet of output one group communication protocol form; Described data communication module, is sent to the network equipment by data packed in data processing module; Be arranged on infrastructure architecture key point place, system will be carried out continuous data acquisition to structural vibration information; The three-dimensional acceleration simulation data-signal collecting amplifies, after filtering processes, by the sample frequency of 10-280Hz, carries out A/D conversion with the form of voltage, converts three-dimensional acceleration numerical value to; Three-dimensional acceleration data, after PSD calculates, are obtained the frequency domain information of vibration, obtain the PSD data that efficiency is higher; PSD data are sent to data center and carry out analyzing and processing, can know clearly the vibration fundamental frequency of infrastructure architecture; Can be used for thus calculating strain mode or strain pulling force, to the long term monitoring of infrastructure architecture vibration fundamental frequency, can directly reflect and measure whether structure changes or extremely.
8. the real-time vibration monitor system of the low-power consumption based on PSD algorithm according to claim 7, it is characterized in that: the Fourier transform in described data processing module and power spectral density PSD computing method: first data are carried out to error checking and memory allocated space, then according to the parameter of configuration, selector channel and selection window are set, use the frequency spectrum in the power spectrum density computing function calculation window that improved discrete fourier transform algorithm forms and preserve transmission calculating end signal after the data of having calculated all windows and passage.
9. the real-time vibration monitor system of the low-power consumption based on PSD algorithm according to claim 7, it is characterized in that: described data communication module adopts ICP/IP protocol and gateway device wired connection to send data, or adopt Zigbee agreement and base station equipment to carry out radio communication transmission data; And in described data communication module transmitting procedure, adopt unified data layout, described data layout comprises Data Identification, timestamp, acceleration direction, sensing data territory.
10. the real-time vibration monitor system of the low-power consumption based on PSD algorithm according to claim 7, is characterized in that: described power module provides stable 5V voltage for whole system.
CN201310689446.5A 2013-12-13 2013-12-13 PSD (power spectral density) algorithm-based low-power-consumption real-time vibration monitoring system and method Pending CN103698003A (en)

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CN105404708A (en) * 2015-10-21 2016-03-16 南京大学 Actually measured acceleration-based outside period motivation and evaluation method for long-span bridge structures
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CN113490267A (en) * 2021-05-18 2021-10-08 浙江传媒学院 Generalized pre-control method for robust stability
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