CN110543618A - roundness uncertainty evaluation method based on probability density function estimation - Google Patents
roundness uncertainty evaluation method based on probability density function estimation Download PDFInfo
- Publication number
- CN110543618A CN110543618A CN201910845682.9A CN201910845682A CN110543618A CN 110543618 A CN110543618 A CN 110543618A CN 201910845682 A CN201910845682 A CN 201910845682A CN 110543618 A CN110543618 A CN 110543618A
- Authority
- CN
- China
- Prior art keywords
- probability density
- roundness
- density function
- uncertainty
- measuring point
- 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.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Data Mining & Analysis (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Physics (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Life Sciences & Earth Sciences (AREA)
- Operations Research (AREA)
- Probability & Statistics with Applications (AREA)
- Bioinformatics & Cheminformatics (AREA)
- Algebra (AREA)
- Evolutionary Biology (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Bioinformatics & Computational Biology (AREA)
- Length Measuring Devices With Unspecified Measuring Means (AREA)
Abstract
The invention provides a roundness uncertainty evaluation method based on probability density function estimation, which comprises the steps of carrying out roundness sampling on a measured object to obtain the collection of a group of measurement point data; fitting a circle according to the measuring point data, and calculating a roundness error; collecting a plurality of groups of measuring point data to obtain a plurality of roundness errors, and taking the plurality of roundness errors as a group of random variables; establishing a random variable probability density function, performing mathematical change on a sample origin moment generated by calculation according to a random variable instead of a theoretical origin moment, and constructing a constraint condition of probability density; taking the original point moment of the sample as a condition, and taking a probability density constraint condition as a target function to obtain a probability density function of the roundness error; and carrying out numerical integration on the probability density function to calculate the standard deviation of the probability density so as to realize uncertainty evaluation of roundness measurement. The method can realize the uncertainty evaluation of the roundness error measurement of the small sample, and has the characteristics of fast algorithm convergence and stable calculation value.
Description
Technical Field
the invention relates to the field of precision metering and computer application, in particular to a roundness uncertainty evaluation method based on probability density function estimation.
Background
The roundness error is used as an important index for evaluating the cylindrical part, and plays an important role in the aspects of precision measuring tools and high-precision error evaluation of the cylindrical part in the fields of mechanical manufacturing, electric power, transportation, aerospace, automatic detection and the like. According to modern error theory, when measuring the size of a workpiece, not only a size measurement result is obtained, but also the uncertainty of the result must be included, and in the new generation of product geometric technical specification (GPS), the measurement uncertainty is called as an execution uncertainty inclusion system. In addition, the evaluation of the uncertainty of the geometric error must be spread out on the basis of the error evaluation.
for uncertainty assessment of roundness errors, past literature was based primarily on the rationale and methodology of the guide to the uncertainty in measurement (GUM) (GUM method) and the monte carlo simulation technique (MCM method). The GUM method needs to calculate the transmission coefficient of each error item and then evaluates the transmission coefficient through a synthesis formula, the calculation process is complex, and particularly when the correlation between errors is difficult to determine, an accurate uncertainty evaluation value is difficult to give. The MCM method is based on the random number principle, although the transfer coefficient and the correlation among errors do not need to be calculated, the probability statistical distribution condition of the measured data needs to be assumed according to experience, and the statistical characteristics of error parameters are evaluated after the data of a large sample is generated. Both methods cannot take into account the evaluation advantages of simplifying calculation and avoiding assumptions for small sample data of roundness error evaluation.
In order to realize uncertainty evaluation with less subjective assumption, at present, probability distribution and parameters of the measurement data are estimated by utilizing the maximum entropy principle to obtain a Probability Density Function (PDF), and then uncertainty of the measurement result is evaluated through numerical calculation. The core problem of the evaluation process is the PDF parameter multivariable optimization problem under the constraint condition derived by the maximum entropy principle, and statistical learning methods such as a gradient descent method, a Newton method or a quasi-Newton method are generally adopted, but the methods all need to consider the problem of objective function derivatives, and the calculation is complicated. In addition, the above studies are mainly directed to measurement uncertainty assessment of single variables, and have not been extended to uncertainty assessment of geometric errors for some time.
in view of the above description, research on an uncertainty evaluation method under the condition of not making a distribution assumption for small sample measurement data with geometric tolerances such as roundness error is very limited, and especially, the process of introducing an intelligent optimization algorithm is very limited.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a roundness uncertainty evaluation method based on probability density function estimation, which can be used for carrying out geometric tolerance uncertainty evaluation and realizing a roundness error uncertainty evaluation process of a small sample and no distribution hypothesis.
The roundness uncertainty evaluation method based on probability density function estimation provided by the invention comprises the following steps:
Step S1: carrying out roundness sampling on the measured object to obtain the collection of a group of measuring point data;
Step S2: fitting a circle according to the measuring point data to obtain a fitting circle center coordinate, and coordinates of a measuring point farthest away from the fitting circle center and a measuring point closest to the fitting circle center, and further calculating a roundness error;
step S3: repeatedly executing the step S1 to collect a plurality of groups of measuring point data, and executing the roundness error calculation of the step S2 on each group of measuring point data respectively to obtain a plurality of roundness errors, wherein the plurality of roundness errors are used as a group of random variables;
step S4: establishing a random variable probability density function, and calculating and generating a sample origin moment instead of a theoretical origin moment according to the random variable to make mathematical change so as to construct a constraint condition of probability density;
Step S5: performing parameter optimization by taking the sample origin moment as a condition and the probability density constraint condition as a target function to obtain unknown parameters of a probability density function, and further obtaining the probability density function of the roundness error;
Step S6: and carrying out numerical integration on the probability density function to calculate the standard deviation of the probability density so as to realize uncertainty evaluation of roundness measurement.
preferably, the sampling method in step S1 specifically includes: if one measuring point is set every 10 degrees, 36 measuring points are set for the circular measured object to obtain a group of measuring point data Pi (xi, yi).
Preferably, step S2 is specifically: and fitting a circle by adopting a least square method according to the measuring point data to obtain a fitting circle center coordinate, a measuring point coordinate farthest away from the fitting circle center and a nearest measuring point coordinate, and further calculating a roundness error.
Preferably, in the step S4, a general form and a constraint condition of the probability density function are constructed through a maximum entropy principle, and a specific construction process is as follows:
step S401: introducing Lagrange multipliers lambda i (i is 1, 2, …, n) into the maximum entropy function,
Wherein, H (x) is an original entropy function, f (x) is a probability density function of a random variable, lambda 0 is a Lagrange multiplier, and n is a positive integer;
step S402: according to the extreme value condition of the maximum entropy function, the following results are obtained:
Step S403: and giving a maximum entropy function constraint condition, wherein the function condition is as follows:
The ith origin moment mi of the sample is:
step S404: the simultaneous (2), (3) and (4) can obtain:
step S405: equation (6) can be regarded as n equation sets containing unknown parameters λ i (i ═ 1, 2, …, n), since the estimation of the unknown parameters according to the roundness error of the known sample has deviation, in order to estimate λ i as accurate as possible, the sum of the squares of the residuals of the true and estimated values can be made as small as possible, and mathematical transformation is performed:
step S406: the residual error ri is recorded and used as a reference,
when the residual sum of squares R is minimal, i.e.:
and obtaining a group of optimal estimated values of lambdai, namely obtaining a probability density function under the condition of maximum entropy.
Preferably, in step S5, when performing parameter optimization by the particle swarm algorithm, the pseudo-maximum number of evolutions of the particle swarm algorithm is set to 100, the population size is set to 30, the variable dimension is 3 consistent with the order of the sample origin moment and corresponds to the setting of the velocity interval, and the particle position interval [ -200, 200] is defined.
preferably, in step S6, the process of calculating the composite posterior distribution f (θ, x) by using the probability density function of the prior distribution and another set of random variables is expressed as:
f(θ，x)＝f(θ)f(x|θ) (10)
Where f (θ) is the prior distribution and f (x | θ) is the probability of another set of random variables, the posterior distribution can be determined by bayesian principles:
in f (x) ═ f (θ) f (x | θ) d θ, the random variable x is fixed, and the posterior distribution can be simplified as:
f(θ|x)∝f(θ)f(x|θ) (12)。
Preferably, in step S6, the roundness measurement uncertainty assessment is achieved by calculating the sample expectation and standard deviation of the random variable by numerical integration.
the method for evaluating the uncertainty of the roundness of the circular surface of the part adopts the method for evaluating the uncertainty of the roundness based on the probability density function estimation.
compared with the prior art, the invention has the following beneficial effects:
the method for evaluating the uncertainty of the roundness error measurement can realize a non-statistical evaluation process of a small sample and no distribution hypothesis, fills the blank of the non-statistical method in national standards, provides a new method for guaranteeing the measurement precision of practical engineering cylindrical parts such as bearings and the like and realizing intelligent evaluation of the uncertainty of the measurement, and has important theoretical significance and social and economic benefits.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a general flow chart of an implementation of the assessment process of the present invention.
FIG. 2 is an iterative flow chart of particle swarm optimization introduced in the invention.
FIG. 3 is a convergence diagram of the particle swarm optimization iteration process in the invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the spirit of the invention. All falling within the scope of the present invention.
In an embodiment of the present invention, the roundness uncertainty evaluation method based on probability density function estimation includes the following steps:
Step S1: and performing roundness sampling on the measured object through a three-coordinate measuring machine to acquire a group of measuring point data.
In the embodiment of the present invention, the specific sampling method is as follows: and setting one measuring point every 10 degrees, and setting 36 measuring points in the circular measured object to obtain a group of measuring points Pi (xi, yi). Pi (xi, yi) is shown in the following table,
| Serial number | X | Y | serial number | X | Y | serial number | X | Y |
| 1 | 8.3572 | -11.3008 | 13 | -13.9484 | -1.7293 | 25 | 5.4804 | 12.8044 |
| 2 | 6.2795 | -12.5886 | 14 | -14.0218 | 0.7224 | 26 | 7.6332 | 11.6543 |
| 3 | 4.0056 | -13.4958 | 15 | -13.6791 | 3.1211 | 27 | 9.5543 | 10.1454 |
| 4 | 1.6219 | -13.9933 | 16 | -12.9064 | 5.4561 | 28 | 11.1890 | 8.3117 |
| 5 | -0.8157 | -14.0706 | 17 | -11.7489 | 7.6081 | 29 | 12.4705 | 6.2460 |
| 6 | -3.2280 | -13.7250 | 18 | -10.2251 | 9.5447 | 30 | 13.3815 | 3.9556 |
| 7 | -5.5392 | -12.9598 | 19 | -8.4031 | 11.1605 | 31 | 13.8733 | 1.5884 |
| 8 | -7.6952 | -11.8073 | 20 | -6.3228 | 12.4433 | 32 | 13.9509 | -0.8663 |
| 9 | -9.6076 | -10.3035 | 21 | -4.0701 | 13.3401 | 33 | 13.6014 | -3.2793 |
| 10 | -11.2532 | -8.4668 | 22 | -1.6816 | 13.8352 | 34 | 12.8572 | -5.5526 |
| 11 | -12.5568 | -6.3425 | 23 | 0.7599 | 13.9117 | 35 | 11.7042 | -7.7191 |
| 12 | -13.4558 | -4.0691 | 24 | 3.1672 | 13.5653 | 36 | 10.1761 | -9.6745 |
step S2: and fitting a circle by adopting a least square method according to the measuring point data to obtain the coordinate of the measuring point with the farthest distance from the fitting circle center and the coordinate of the nearest measuring point, and further calculating the roundness error.
in the embodiment of the invention, the coordinates of the fitting circle center are (-0.0348, -0.077), and the calculated roundness error is 0.0099 mm.
step S3: and (4) repeatedly executing the step (S1) to collect a plurality of groups of measuring point data, and executing the roundness error calculation of the step (S2) on each group of measuring point data respectively to obtain the small sample roundness error as a group of random variables.
In the embodiment of the present invention, if the number of the sets of measurement point data is 10, 10 roundness errors are generated, which is specifically shown in the following table:
| serial number | 1 | 2 | 3 | 4 | 5 |
| roundness error delta | 0.0099 | 0.0081 | 0.0091 | 0.0023 | 0.0028 |
| serial number | 6 | 7 | 8 | 9 | 10 |
| Roundness error delta | 0.0064 | 0.0036 | 0.0075 | 0.0094 | 0.0076 |
Step S4: the general form and the constraint condition of the probability density function are constructed according to the maximum entropy principle, and the specific construction process is as follows:
Step S401: introducing Lagrange multipliers lambda i (i is 1, 2, …, n) into the maximum entropy function,
wherein, H (x) is the original entropy function, f (x) is the probability of random variable
And the density function is that lambda 0 is a Lagrange multiplier and n is a positive integer.
step S402: according to the extreme value condition of the maximum entropy function, the following results are obtained:
step S403: and giving a maximum entropy function constraint condition, wherein the function condition is as follows:
The ith origin moment mi of the sample is:
Step S404: the simultaneous (2), (3) and (4) can obtain:
step S405: equation (6) can be regarded as n equation sets containing unknown parameters λ i (i ═ 1, 2, …, n), since the unknown parameters are estimated according to the roundness error of the known sample, the estimated values of the unknown parameters have deviations, and in order to estimate λ i as accurate as possible, the sum of the squares of the residuals of the real values and the estimated values can be made as small as possible, so as to perform mathematical transformation:
Step S406: the residual error ri is recorded and used as a reference,
when the residual sum of squares R is minimal, i.e.:
And obtaining a group of optimal estimated values of lambdai, namely obtaining a probability density function under the condition of maximum entropy.
In the embodiment of the present invention, the maximum entropy principle constructs a general form and a constraint condition of a probability density function, and first determines an integration interval [0.0023, 0.0099], takes a third-order sample moment as a maximum entropy condition, and calculates a third-order origin moment mi of 10 sets of circularity error samples in step S3 as [0.0067, 5.1585e +05, 4.2897e +07], as a maximum entropy constraint. The general form of the roundness error PDF at third order is:
step S5: and jumping to serve as a target function according to probability density constraint constructed in the step S4, taking the random variable as a sample value, introducing a particle swarm algorithm to carry out parameter optimization, setting the quasi-maximum evolutionary number of the particle swarm algorithm to be 100, setting the population scale to be 30, setting the variable dimension to be consistent with the order of the sample origin moment to be 3, corresponding to the setting of a speed interval, limiting particle position intervals [ -200, 200], solving the optimal estimation of lambdai, and further estimating a probability density function f (x) of the roundness error under the sample.
in the embodiment of the present invention, λ i is [171.4036, 166.2738, 110.7145], and λ 0 is calculated as 3.7556, and the round degree error PDF obtained by substituting the PDF in the step 4 in a general form of the measured value sample is:
f(x)＝exp(3.7556+171.4036x+166.2738x+110.7145x)
step S6: the measurement uncertainty u of the roundness error may be 0.0021mm by integrating the PDF value estimated in step S5.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention.
Claims (8)
1. a roundness uncertainty evaluation method based on probability density function estimation is characterized by comprising the following steps:
Step S1: carrying out roundness sampling on the measured object to obtain the collection of a group of measuring point data;
step S2: fitting a circle according to the measuring point data to obtain a fitting circle center coordinate, and coordinates of a measuring point farthest away from the fitting circle center and a measuring point closest to the fitting circle center, and further calculating a roundness error;
Step S3: repeatedly executing the step S1 to collect a plurality of groups of measuring point data, and executing the roundness error calculation of the step S2 on each group of measuring point data respectively to obtain a plurality of roundness errors, wherein the plurality of roundness errors are used as a group of random variables;
step S4: establishing a random variable probability density function, and calculating and generating a sample origin moment instead of a theoretical origin moment according to the random variable to make mathematical change so as to construct a constraint condition of probability density;
step S5: performing parameter optimization by taking the sample origin moment as a condition and the probability density constraint condition as a target function to obtain unknown parameters of a probability density function, and further obtaining the probability density function of the roundness error;
Step S6: and carrying out numerical integration on the probability density function to calculate the standard deviation of the probability density so as to realize uncertainty evaluation of roundness measurement.
2. The method for evaluating the uncertainty of the circularity based on the probability density function estimation according to claim 1, wherein the sampling method in the step S1 is specifically: if one measuring point is set every 10 degrees, 36 measuring points are set for the circular measured object to obtain a group of measuring point data Pi (xi, yi).
3. the method for evaluating the uncertainty of the circularity based on the probability density function estimation according to claim 1, wherein the step S2 is specifically: and fitting a circle by adopting a least square method according to the measuring point data to obtain a fitting circle center coordinate, a measuring point coordinate farthest away from the fitting circle center and a nearest measuring point coordinate, and further calculating a roundness error.
4. the method for evaluating the uncertainty of the circularity based on the probability density function estimation of claim 1, wherein the general form and the constraint condition of the probability density function are constructed by the maximum entropy principle in the step S4, and the specific construction process is as follows:
Step S401: introducing Lagrange multipliers lambda i (i is 1, 2, …, n) into the maximum entropy function,
wherein, H (x) is an original entropy function, f (x) is a probability density function of a random variable, lambda 0 is a Lagrange multiplier, and n is a positive integer;
step S402: according to the extreme value condition of the maximum entropy function, the following results are obtained:
Step S403: and giving a maximum entropy function constraint condition, wherein the function condition is as follows:
The ith origin moment mi of the sample is:
step S404: the simultaneous (2), (3) and (4) can obtain:
step S405: equation (6) can be regarded as n equation sets containing unknown parameters λ i (i ═ 1, 2, …, n), since the estimation of the unknown parameters according to the roundness error of the known sample has deviation, in order to estimate λ i as accurate as possible, the sum of the squares of the residuals of the true and estimated values can be made as small as possible, and mathematical transformation is performed:
Step S406: the residual error ri is recorded and used as a reference,
When the residual sum of squares R is minimal, i.e.:
and obtaining a group of optimal estimated values of lambdai, namely obtaining a probability density function under the condition of maximum entropy.
5. the method for evaluating the degree of uncertainty of the circularity based on the probability density function estimation of claim 1, wherein in step S5, when the parameter optimization is performed by the particle swarm algorithm, the pseudo-maximum number of evolutions of the particle swarm algorithm is set to 100, the population size is set to 30, the variable dimension is 3 in accordance with the order of the sample origin moment, and the particle position interval [ -200, 200] is defined in correspondence with the setting of the velocity interval.
6. The method for evaluating the uncertainty of the circularity based on the probability density function estimation according to claim 1, wherein in step S6, the process of calculating the composite posterior distribution f (θ, x) from the prior distribution and the probability density function of another set of random variables is represented as:
f(θ，x)＝f(θ)f(x|θ) (10)
Where f (θ) is the prior distribution and f (x | θ) is the probability of another set of random variables, the posterior distribution can be determined by bayesian principles:
in f (x) ═ f (θ) f (x | θ) d θ, the random variable x is fixed, and the posterior distribution can be simplified as:
f(θ|x)∝f(θ)f(x|θ) (12)。
7. The method for evaluating the uncertainty of the circularity based on the probability density function estimation of claim 1, wherein in step S6, the uncertainty of the circularity measurement is evaluated by calculating the sample expectation and the standard deviation of the random variable through numerical integration.
8. a method for evaluating the uncertainty of the roundness of a circular surface of a part, characterized by using the method for evaluating the uncertainty of the roundness based on the probability density function estimation according to any one of claims 1 to 7.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910845682.9A CN110543618A (en) | 2019-09-05 | 2019-09-05 | roundness uncertainty evaluation method based on probability density function estimation |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910845682.9A CN110543618A (en) | 2019-09-05 | 2019-09-05 | roundness uncertainty evaluation method based on probability density function estimation |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN110543618A true CN110543618A (en) | 2019-12-06 |
Family
ID=68712930
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910845682.9A Pending CN110543618A (en) | 2019-09-05 | 2019-09-05 | roundness uncertainty evaluation method based on probability density function estimation |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110543618A (en) |
Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110567421A (en) * | 2019-09-05 | 2019-12-13 | 上海应用技术大学 | dynamic roundness uncertainty evaluation method based on Bayesian principle |
| CN111046579A (en) * | 2019-12-26 | 2020-04-21 | 哈尔滨工业大学 | Large-scale high-speed rotation equipment error separation optimization method based on particle swarm optimization |
| CN111553077A (en) * | 2020-04-29 | 2020-08-18 | 大连理工大学 | Method for evaluating uncertainty of on-machine measurement |
| CN112733459A (en) * | 2021-01-20 | 2021-04-30 | 湖南科技大学 | Robust estimation method, device and medium for probability integration method parameter based on CA-rPSO |
| US11288602B2 (en) | 2019-09-18 | 2022-03-29 | Hartford Steam Boiler Inspection And Insurance Company | Computer-based systems, computing components and computing objects configured to implement dynamic outlier bias reduction in machine learning models |
| US11328177B2 (en) | 2019-09-18 | 2022-05-10 | Hartford Steam Boiler Inspection And Insurance Company | Computer-based systems, computing components and computing objects configured to implement dynamic outlier bias reduction in machine learning models |
| US11334645B2 (en) | 2011-08-19 | 2022-05-17 | Hartford Steam Boiler Inspection And Insurance Company | Dynamic outlier bias reduction system and method |
| US11550874B2 (en) | 2014-04-11 | 2023-01-10 | Hartford Steam Boiler Inspection And Insurance Company | Future reliability prediction based on system operational and performance data modelling |
| US11615348B2 (en) | 2019-09-18 | 2023-03-28 | Hartford Steam Boiler Inspection And Insurance Company | Computer-based systems, computing components and computing objects configured to implement dynamic outlier bias reduction in machine learning models |
| US11636292B2 (en) | 2018-09-28 | 2023-04-25 | Hartford Steam Boiler Inspection And Insurance Company | Dynamic outlier bias reduction system and method |
| CN111046579B (en) * | 2019-12-26 | 2024-05-31 | 哈尔滨工业大学 | Error separation optimization method for large-scale high-speed rotation equipment based on particle swarm optimization |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101493321A (en) * | 2009-02-18 | 2009-07-29 | 上海理工大学 | Planarity assessment method for decreasing number of measuring points |
| CN104008304A (en) * | 2014-06-10 | 2014-08-27 | 北京航空航天大学 | An evaluation method of uncertainty in the entropy measurement for multisensor neural network of poor information |
| CN105989241A (en) * | 2016-01-18 | 2016-10-05 | 合肥工业大学 | Bayesian information fusion-based measurement uncertainty evaluation and real-time updating method |
-
2019
- 2019-09-05 CN CN201910845682.9A patent/CN110543618A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101493321A (en) * | 2009-02-18 | 2009-07-29 | 上海理工大学 | Planarity assessment method for decreasing number of measuring points |
| CN104008304A (en) * | 2014-06-10 | 2014-08-27 | 北京航空航天大学 | An evaluation method of uncertainty in the entropy measurement for multisensor neural network of poor information |
| CN105989241A (en) * | 2016-01-18 | 2016-10-05 | 合肥工业大学 | Bayesian information fusion-based measurement uncertainty evaluation and real-time updating method |
Non-Patent Citations (3)
| Title |
|---|
| MOSCHOS PAPANANIAS.ET.AL.: "A Bayesian framework to estimate part quality and associated uncertainties in multistage manufacturing", 《COMPUTERS IN INDUSTRY》 * |
| 吴福仙等: "极大似然最大熵概率密度估计及其优化解法", 《南京航空航天大学学报》 * |
| 张珂等: "圆度误差的神经网络评定及测量不确定度研究", 《机械科学与技术》 * |
Cited By (14)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US11334645B2 (en) | 2011-08-19 | 2022-05-17 | Hartford Steam Boiler Inspection And Insurance Company | Dynamic outlier bias reduction system and method |
| US11550874B2 (en) | 2014-04-11 | 2023-01-10 | Hartford Steam Boiler Inspection And Insurance Company | Future reliability prediction based on system operational and performance data modelling |
| US11803612B2 (en) | 2018-09-28 | 2023-10-31 | Hartford Steam Boiler Inspection And Insurance Company | Systems and methods of dynamic outlier bias reduction in facility operating data |
| US11636292B2 (en) | 2018-09-28 | 2023-04-25 | Hartford Steam Boiler Inspection And Insurance Company | Dynamic outlier bias reduction system and method |
| CN110567421A (en) * | 2019-09-05 | 2019-12-13 | 上海应用技术大学 | dynamic roundness uncertainty evaluation method based on Bayesian principle |
| US11328177B2 (en) | 2019-09-18 | 2022-05-10 | Hartford Steam Boiler Inspection And Insurance Company | Computer-based systems, computing components and computing objects configured to implement dynamic outlier bias reduction in machine learning models |
| US11288602B2 (en) | 2019-09-18 | 2022-03-29 | Hartford Steam Boiler Inspection And Insurance Company | Computer-based systems, computing components and computing objects configured to implement dynamic outlier bias reduction in machine learning models |
| US11615348B2 (en) | 2019-09-18 | 2023-03-28 | Hartford Steam Boiler Inspection And Insurance Company | Computer-based systems, computing components and computing objects configured to implement dynamic outlier bias reduction in machine learning models |
| CN111046579A (en) * | 2019-12-26 | 2020-04-21 | 哈尔滨工业大学 | Large-scale high-speed rotation equipment error separation optimization method based on particle swarm optimization |
| CN111046579B (en) * | 2019-12-26 | 2024-05-31 | 哈尔滨工业大学 | Error separation optimization method for large-scale high-speed rotation equipment based on particle swarm optimization |
| CN111553077B (en) * | 2020-04-29 | 2022-10-04 | 大连理工大学 | Method for evaluating uncertainty of on-machine measurement |
| CN111553077A (en) * | 2020-04-29 | 2020-08-18 | 大连理工大学 | Method for evaluating uncertainty of on-machine measurement |
| CN112733459B (en) * | 2021-01-20 | 2022-04-12 | 湖南科技大学 | Robust estimation method, device and medium for probability integration method parameter |
| CN112733459A (en) * | 2021-01-20 | 2021-04-30 | 湖南科技大学 | Robust estimation method, device and medium for probability integration method parameter based on CA-rPSO |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110543618A (en) | roundness uncertainty evaluation method based on probability density function estimation | |
| Wen et al. | Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error | |
| da Silva Hack et al. | Measurement uncertainty: Literature review and research trends | |
| Schwenke et al. | Assessment of uncertainties in dimensional metrology by Monte Carlo simulation: proposal of a modular and visual software | |
| CN112697041B (en) | Monte carlo method-based pre-evaluation method for measurement accuracy of assembly pose | |
| CN104853435A (en) | Probability based indoor location method and device | |
| CN111553077B (en) | Method for evaluating uncertainty of on-machine measurement | |
| GB2330206A (en) | Determining the uncertainty of a coordinate measuring machine | |
| CN110567421B (en) | Dynamic roundness uncertainty evaluation method based on Bayesian principle | |
| Cheng et al. | Analysis and comparison of Bayesian methods for measurement uncertainty evaluation | |
| Pathak et al. | Form error evaluation of noncontact scan data using constriction factor particle swarm optimization | |
| CN109188481A (en) | A kind of new method being fitted GPS height anomaly | |
| Wen et al. | Monte Carlo method for the uncertainty evaluation of spatial straightness error based on new generation geometrical product specification | |
| CN113360983A (en) | Slope reliability analysis and risk assessment method | |
| Gu et al. | A robust moving total least-squares fitting method for measurement data | |
| CN115470672A (en) | Spatial residual stress reconstruction method | |
| Bulutsuz et al. | Application of fuzzy logic methodology for predicting dynamic measurement errors related to process parameters of coordinate measuring machines | |
| CN109508482A (en) | A kind of calculation method for complex-curved surface profile degree error uncertainty | |
| CN113513978B (en) | High-precision measurement method and system for relative change of end face pose in high-temperature and low-temperature environment | |
| Cao et al. | A study on mutative scale straightness measurement based on uncertainty analysis | |
| Chen et al. | Thermal error modeling of CNC machine tool spindle based on multiple regression and features selection | |
| Cheng et al. | Selection and modeling of temperature variables for the thermal error compensation in servo system | |
| CN109871608B (en) | Uncertainty analysis method for curved surface measurement positioning error | |
| Sun et al. | Analysis and inference of stream of dimensional errors in multistage machining process based on an improved semiparametric model | |
| Franaszek et al. | Gauging the repeatability of 3-d imaging systems by sphere fitting |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |