CN115758754A - Energy-saving optimization method for accelerated life test of axial plunger pump - Google Patents
Energy-saving optimization method for accelerated life test of axial plunger pump Download PDFInfo
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Abstract
The invention discloses an energy-saving optimization method for an acceleration life test of an axial plunger pump, which comprises the following steps: (1) Establishing an energy consumption model of an axial plunger pump accelerated life test as a target function; (2) Obtaining accuracy evaluation values of different accelerated life test schemes by using a Monte Carlo random simulation method, and fitting probability distribution of the accuracy evaluation values; (3) And optimizing an accelerated life test scheme by combining a life evaluation accuracy threshold and adopting a multi-target stochastic programming solving method. The constant pressure accelerated life test based on the simulation method can give consideration to energy conservation and test accuracy, and an optimal solution is obtained by combining multi-objective optimization, so that the energy conservation optimization is realized while the accuracy of test evaluation is ensured.
Description
Technical Field
The invention relates to the field of axial plunger pump service life tests, in particular to an energy-saving optimization method for an axial plunger pump accelerated service life test.
Background
The hydraulic transmission system has the advantages of small volume, high power, high precision, fast response, strong anti-interference capability and the like, and is widely applied to various fields of agriculture and forestry machinery, metallurgical machinery, chemical machinery, engineering machinery, war industry, ships, aerospace and the like. The axial plunger pump serves as a core element for powering the hydraulic transmission system and is called the "heart" of the hydraulic system. Meanwhile, the axial plunger pump is used as a key hydraulic element in a hydraulic system, and has the characteristics of long service life, high efficiency, high reliability and the like, if the plunger pump is subjected to a service life test under rated pressure or normal service pressure by adopting traditional reliability evaluation, not only is a large amount of test expenditure and test time consumed, but also the condition of no failure sample can still occur even after a long-time reliability service life test. Therefore, in order to evaluate the service life and the reliability level of the axial plunger pump in a short time, a reliability accelerated service life test method can be adopted to shorten the test time of the axial plunger pump compared with the test time under normal test pressure, greatly reduce the development cost and meet the requirement of the host development progress.
The accelerated life test is a life test method which is characterized in that a product breaks down in a short time by adopting a method of improving working pressure or other external pressure on the basis of reasonable engineering technology and mathematical statistics, and reliability indexes of the product at a normal pressure level are deduced by using test data information obtained under accelerated pressure. In short, the accelerated life test is a life test method for accelerating the failure of a product at a high pressure level under the condition of keeping the failure mechanism unchanged; the method aims to acquire test data in a short time, analyze the failure mechanism reason of a product, and then construct an acceleration model between the service life and the stress so as to extrapolate the characteristic service life under the normal stress.
The reliability accelerated life test can be divided into the following steps according to the loading mode of the test pressure: three acceleration test modes of a constant pressure acceleration life test, a stepping pressure acceleration life test and a sequential pressure acceleration life test. The three accelerated life test methods have respective advantages and disadvantages aiming at different test scheme requirements. The constant pressure accelerated life test refers to that a sample is tested under a constant accelerated pressure level as the name implies; the step pressure accelerated life test refers to that after a sample is tested for a period of time under an accelerated pressure level, the pressure is increased again for testing, and the pressure applied by the sequential accelerated test on the basis of the step accelerated test is in direct proportion to the time. Therefore, compared with other two test modes, the constant pressure accelerated life test has the defects of long time, large required sample amount, high test cost and the like. However, the operation method of the constant pressure accelerated life test is simple from the consideration of the practical test operation mode and the analysis and statistics of test data, the theoretical guidance of the test data is mature, and the reliability statistical evaluation precision is higher.
In the accelerated life test, the design of the reasonable test scheme can not only improve the product life evaluation precision, but also optimize the test cost, the energy consumption and the like. Von snow peak is based on a Weibull distribution model in reliability statistical analysis and optimization design scheme based on accelerated life test data, pressure level number, pressure level size, sample size proportion and tail cutting time are used as optimization variables, and the life progressive variance minimization is used as a criterion, so that the accelerated life optimization design with constant pressure at regular time and tail cutting is performed. When the Weibull distribution parameter pair test precision is neglected in the Optimal design of life testing cost model for Type-II centering Weibull distribution time units and response to unknown parameters by Cordeiro, the sample amount is used as a decision variable, the test cost is used as a target function, and the fixed number truncated accelerated life test cost is minimized by optimizing the sample amount. Mann provides a least square curve fitting characteristic life method in Design of over-stress life-test experiments and the two parameter Weibull distribution, and the optimized Design of the cycle pressure accelerated life test is realized by optimizing the pressure level series and the sample distribution proportion of each pressure level. The accelerated life test design scheme optimizes the test cost and the test evaluation precision by taking the accelerated test pressure number, the test sample number, the tail cutting time and the like as decision variables.
Disclosure of Invention
The invention aims to provide a method for evaluating and optimizing a constant-pressure accelerated life test scheme of an axial plunger pump, which solves the problems of high energy consumption and long time consumption of the traditional plunger pump life test in the background art, can give consideration to both energy conservation and test accuracy by combining multi-objective optimization to obtain an optimal solution based on the constant-pressure accelerated life test of a simulation method, thereby realizing energy conservation optimization while ensuring the accuracy of test evaluation.
In order to achieve the purpose, the invention provides the following technical scheme:
an energy-saving optimization method for an axial plunger pump accelerated life test comprises the following steps:
(1) Establishing an energy consumption model of an axial plunger pump accelerated life test as a target function E;
(2) Obtaining accuracy evaluation values of different accelerated life test schemes by using a Monte Carlo random simulation method, and fitting probability distribution of the accuracy evaluation values;
(3) And optimizing an accelerated life test scheme by combining the threshold of the life evaluation accuracy and adopting a multi-target stochastic programming solving method.
The energy consumption model in the step (1) is determined by a test pressure value S i Average life T of test specimen i The number K of test samples, the number L of test pressure steps, and the flow rate Q. The energy consumption model of the axial plunger pump is specifically represented by the formula (1):
wherein i represents the ith stage pressure level, i.e., the ith set of tests, and i =1, 2.., L; k i Representing the number of test samples at the i-th stage pressure level; s. the i Represents the ith stage pressure value; t is a unit of i For testing samplesAt S i Average life when failure occurs under pressure. The model assumes a sample number K for each pressure class i For a constant value K, if the flow Q is constant for a fixed displacement pump at different pressures, equation (1) can be simplified to
Further, the accuracy evaluation is performed on the combined optimization variables by adopting scene analysis in the step (2), and the specific steps are as follows:
step 01: inputting simulation test parameters of the plunger pump, including parameters a and b of an acceleration model, a service life distribution parameter sigma, a test pressure grade number L (L is more than or equal to 2), a test sample number K under each test pressure grade, and upper and lower limits Sa of the test pressure max And Sa min The total scene number p and the total simulation times Z in each scene. The acceleration model between test pressure and mean life is assumed to be as follows:
T i ＝a+b×S i (3)
in the formula, T i Is S i Mean value of the corresponding distribution parameter under test pressure, S i The test pressure. Therefore, the normal pressure S can be calculated on the premise that the values of the parameters a and b are known 0 Average life T of the grade 0 As a reference lifetime.
Step 02: under the premise of not changing the failure mechanism of the plunger pump, a step stress acceleration test method is adopted to gradually determine a test pressure interval Sa min ,Sa max ]Then, selecting L values at equal intervals in the pressure interval as test pressure values Sa (i) of each test pressure grade, wherein the average service life of the pressure interval corresponding to each test pressure grade is Ta (i) = a + b × Sa (i), and i is more than or equal to 1 and less than or equal to i<L。
Step 03: assuming that the sample life points of the plunger pump at each test pressure level are mutually independent and are normally distributed, a monte carlo sampling method can be used in combination with the step 2 to obtain random samples at each test pressure level, and Z times of simulation cycles are carried out. Namely, it is
t～normrnd(T a (i),σ,K,1) (4)
Where K is the sample size at each test pressure level and σ is the standard deviation of the lifetime distribution.
Step 04: according to the pressure S of the plunger pump at each accelerated test i Number of K simulation failure samples generated at the bottom, t = (t) 1 ,t 2 ,...t k ) The simulated failure data at each pressure are re-fitted and distributed to obtain (
σ)
Step 05: using multiple sets (S) based on all samples according to a linear relationship between stress and mean life in the acceleration model i ，
) Acceleration model coefficient estimation value based on simulation is obtained by using least square method and linear regression
Will S 0 Substituting into the acceleration model to obtain the average life under normal test pressure
Step 06: average service life T of plunger pump based on normal test pressure 0 And the average service life of the plunger pump obtained by accelerated test optimization
The relative percent error (RPD) was calculated, the RPD with the largest absolute value being the RPD under this test protocol:
and 07, repeating the steps 03 to 06 until the preset simulation times Z. And taking the maximum value in the Z simulation scheme as the final RPD of the simulation in the scene, and then entering the step 8.
And 08, repeating the steps 03 to 07 until the scene number is larger than p and ending. Thereby obtaining p RPDs corresponding to a test design scheme L,k
Further, the step (3) adopts a multi-objective stochastic programming solving method, and the specific steps for optimizing the accelerated life test scheme are as follows:
09, RPD according to the multi-scene target value under each variable combination L,k Fitting probability distribution to obtain the distributed parameters under each variable combination;
step 10, a threshold value of a specific target function and RPDth are given, and the cumulative probability P (RPD is less than or equal to RPDth) meeting the threshold value under each variable combination is determined according to the parameters of fitting distribution;
and 11, sequencing all variable combinations according to the target function energy consumption E of the plunger pump constructed in the foregoing. And then obtaining the conditional probability of each variable combination of the multi-target optimal solution, and taking the expected value of one group or all combinations with the maximum probability as the final optimal solution.
Compared with the prior art, the invention has the beneficial effects that:
the invention solves the problem of high cost of the previous constant accelerated life test of the plunger pump, provides an energy-saving optimization method for the accelerated life test of the axial plunger pump based on scene analysis, aims to improve the test accuracy and reduce the test energy consumption, applies a solving method of random multi-objective planning, provides a test optimization solution, reduces the test energy consumption and reduces the test cost, thereby improving the economic benefit of hydraulic enterprises, providing reliable technical support and guarantee for the performance test of core hydraulic elements in China, and providing theoretical and practical references for reducing the reliability difference between the core hydraulic elements in China and other developed industrial countries in the world.
The invention designs a constant pressure accelerated life test scheme optimization method which gives consideration to energy saving and test accuracy from the viewpoints of test energy consumption and test accuracy and is based on a constant pressure accelerated life test of a simulation method.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of the accelerated life test principle of the axial plunger pump based on scene analysis.
FIG. 3 is a schematic diagram of an optimization solution of an accelerated life test of an axial plunger pump based on scene analysis.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 to 3, the present invention provides a technical solution:
an energy-saving optimization method for an axial plunger pump accelerated life test comprises the following steps:
(1) Establishing an energy consumption model of an axial plunger pump accelerated life test as a target function E;
(2) Obtaining accuracy evaluation values of different accelerated life test schemes by using a Monte Carlo random simulation method, and fitting probability distribution of the accuracy evaluation values;
(3) And optimizing an accelerated life test scheme by combining the threshold of the life evaluation accuracy and adopting a multi-target stochastic programming solving method.
The energy consumption model in the step (1) is determined by a test pressure value S i Average life T of test specimen i The number K of test samples, the number L of test pressure steps, and the flow rate Q. The energy consumption model of the axial plunger pump is specifically represented by the formula (1):
wherein i represents the ith stage pressure level, i.e. the ith group of tests, and i =1, 2., L; k i Representing the number of test samples at the i-th stage pressure level; s i Representing the pressure value of the ith grade; t is i For the test specimen at S i Average life when failure occurs under pressure. The model assumes a sample number K for each pressure class i For a constant value K, if the flow Q is constant at different pressures for a fixed displacement pump, equation (1) can be simplified to a constant value
The accelerated life test of the plunger pump is similar to the life test method process, firstly, the failure threshold value of the plunger pump is set before the test, then the volumetric efficiency, the leakage oil return quantity or the wear quantity of a sliding shoe and the like of the plunger pump are used as monitoring quantities in the test process, the monitoring quantities reach the failure threshold value in a short time by increasing the pressure, so that the characteristic life of the plunger pump under high horizontal pressure is obtained, and finally, the characteristic life under normal stress is obtained by utilizing an accelerated model to extrapolate. Therefore, the factors influencing the reliability life accuracy under normal pressure discovered by the accelerated life test principle comprise: test pressure, test pressure grade number, and sample number under each test pressure grade. And by optimizing the decision variable values, reference is provided for the accelerated life test of the plunger pump.
In the step (2), the accuracy evaluation is performed on the combined optimization variables by adopting scene analysis, and the method specifically comprises the following steps:
step 01: inputting simulation test parameters of the plunger pump, including parameters a and b of an acceleration model, a service life distribution parameter sigma, a test pressure grade number L (L is more than or equal to 2), a test sample number K under each test pressure grade, and upper and lower limits Sa of test pressure max 、Sa min Total number of scenes p and total number of simulations Z per scene. The acceleration model between the test pressure and the mean life is assumed to be as follows:
T i ＝a+b×S i (3)
in the formula, T i Is S i Mean value of the corresponding distribution parameter under test pressure, S i The test pressure. Therefore, the normal pressure S can be calculated under the premise that the values of the parameters a and b are known 0 Mean life T of the grade 0 As a reference lifetime.
Step 02: under the premise of not changing the failure mechanism of the plunger pump, a step pressure accelerated life test method is adopted to gradually determine a test pressure interval Sa min ,Sa max ]Then, L values are selected at equal intervals in the pressure interval as test pressure values Sa (i) of each test pressure level, the average life of the pressure interval corresponding to each test pressure level is Ta (i) = a + b × Sa (i), and 1 ≦ i<L。
And 03: assuming that the sample life points of the plunger pump at each test pressure level are mutually independent and obey normal distribution, a Monte Carlo sampling method can be used in combination with the step 2 to obtain random samples at each test pressure level, and Z times of simulation cycles are carried out. Namely that
t~normrnd(T a (i),σ,K,1) (4)
K is the sample size at each test pressure level and σ is the standard deviation of the lifetime distribution.
Step 04: according to the pressure S of the plunger pump at each accelerated test i Number of K simulation failure samples generated at the bottom, t = (t) 1 ,t 2 ,...t k ) The simulated failure data at each pressure are re-fitted and distributed to obtain (
σ)
Step 05: using multiple sets (S) based on all samples according to a linear relationship between stress and mean life in the acceleration model i ，
) Acceleration model coefficient estimation value based on simulation is obtained by using least square method and linear regression
Will S 0 Substituting into the acceleration model to obtain the average life under normal test pressure
Step 06: average service life T of plunger pump based on normal test pressure 0 And the average service life of the plunger pump obtained by accelerated test optimization
Calculating a relative percentage error (relative percentage error)
devision, RPD), the largest absolute value as the RPD under this protocol:
and step 07, repeating the steps 03 to 06 until the simulation times Z are preset. And taking the maximum value in the Z-time simulation scheme as the final RPD of the simulation in the scene, and then entering the step 8.
And 08, repeating the steps 03 to 07 until the scene number is more than p, and ending. Thereby obtaining p RPDs corresponding to a test design scheme L,k 。
The step (3) adopts a multi-objective stochastic programming solving method, and the specific steps for optimizing the accelerated life test scheme are as follows:
step 09, RPD according to the multi-scenario target value under each variable combination L,k Fitting probability distribution to obtain the distributed parameters under each variable combination;
step 10, a threshold value of a specific target function and RPDth are given, and the cumulative probability P (RPD is less than or equal to RPDth) meeting the threshold value under each variable combination is determined according to the parameters of fitting distribution;
and 11, sequencing all variable combinations according to the target function energy consumption E of the plunger pump constructed in the foregoing. And then obtaining the conditional probability of each variable combination of the multi-target optimal solution, and taking the expected value of one group or all combinations with the maximum probability as the final optimal solution.
The invention provides a constant-pressure accelerated life test energy-saving optimization method aiming at the problems of high energy consumption and long time in a plunger pump life test, and the method is used for optimizing test accuracy and energy consumption in the life test. The main technical key lies in that:
(1) And (3) utilizing a Monte Carlo simulation method to obtain the reliability life by combining different pressure grade numbers and sample numbers and carrying out accuracy evaluation.
(2) And solving the energy consumption and the test accuracy by the random multi-target programming based on scene analysis.
The invention takes the simulation test of the axial plunger pump as an example to illustrate the effectiveness of the energy-saving optimization method for the constant-pressure accelerated life test of the axial plunger pump. And by using a test scheme of a group test, the test pressure grade number, the sample number under each test pressure grade, the test pressure and the like in the test are used as decision variables to optimize the test accuracy and reduce the energy consumption.
Compared with the prior art, the method has the technical effects that aiming at the problems of high energy consumption and long consumed time of the traditional plunger pump life test, the method for comprehensively optimizing two mutually exclusive targets of the energy consumption and the test accuracy of the life test is provided, and the method is combined with multi-objective optimization to calculate the optimal solution, so that the accuracy of test evaluation is ensured, and meanwhile, the energy-saving optimization is realized.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (3)
1. An energy-saving optimization method for an axial plunger pump accelerated life test is characterized by comprising the following steps:
(1) Establishing an energy consumption model of an axial plunger pump accelerated life test as a target function E;
(2) Obtaining accuracy evaluation values of different accelerated life test schemes by using a Monte Carlo random simulation method, and fitting probability distribution of the accuracy evaluation values;
(3) Optimizing an accelerated life test scheme by combining a life evaluation accuracy threshold and adopting a multi-target random programming solving method;
the energy consumption model in the step (1) is determined by a test pressure value S i Average life T of test specimen i The number K of test samples, the number L of test pressure stages and the flow Q; the energy consumption model of the axial plunger pump is as follows:
wherein i represents the ith stage pressure level, i.e., the ith set of tests, and i =1, 2.., L; k i Representing the number of test samples at the i-th stage pressure level; s i Representing the pressure value of the ith grade; t is i For the test specimen at S i Average life when failure occurs under pressure; the model assumes a sample number K for each pressure class i Is a constant value K, if the flow Q is a constant value under different pressures for the fixed displacement pump, the energy consumption model of the axial plunger pump can be simplified to be
2. The energy-saving optimization method for the accelerated life test of the axial plunger pump according to claim 1, characterized in that: in the step (2), the accuracy evaluation is performed on the combined optimization variables by adopting scene analysis, and the method specifically comprises the following steps:
step 01: inputting simulation test parameters of the plunger pump, including parameters a and b of an acceleration model, a service life distribution parameter sigma, a test pressure grade number L (L is more than or equal to 2), and the number of test samples under each test pressure gradeK. Upper and lower limits Sa of test pressure max And Sa min The total scene number p and the total simulation times Z in each scene; the acceleration model between test pressure and mean life is assumed to be as follows:
T i ＝a+b×S i
in the formula, T i Is S i The corresponding mean life under test pressure, and also the mean value of the life distribution parameter, S i The test pressure. Therefore, under the premise that the values of the parameters a and b are known, the normal pressure S can be calculated 0 Mean life T of the grade 0 As a reference life;
step 02: under the premise of not changing the failure mechanism of the plunger pump, the test pressure interval [ Sa ] is determined step by the method of the step stress acceleration test min ,Sa max ]Then, selecting L values at equal intervals in the pressure interval as test pressure values Sa (i) of each test pressure grade, wherein the average service life of the pressure interval corresponding to each test pressure grade is Ta (i) = a + b × Sa (i), and i is more than or equal to 1 and less than or equal to i<L；
And 03: assuming that the sample life points of the plunger pump at each test pressure level are mutually independent and are normally distributed, the random sample at each test pressure level can be obtained by utilizing the Monte Carlo sampling method in combination with the step 2, and Z times of simulation circulation is carried out, namely
t～normrnd(T a (i),σ,K,1)
Wherein, K is the sample size under each test pressure grade, and sigma is the standard deviation of the service life distribution;
step 04: according to the pressure S of the plunger pump at each accelerated test i Number of K simulation failure samples generated at the bottom, t = (t) 1 ,t 2 ,...t k ) And the failure data simulated under each pressure is re-fitted and distributed to obtain
Step 05: utilizing multiple sets based on all samples according to a linear relationship between stress and mean life in an acceleration model
Acceleration model coefficient estimation value based on simulation is obtained by using least square method and linear regression
Will S 0 Substituting into the acceleration model to obtain the average life under normal test pressure
Step 06: average service life T of plunger pump based on normal test pressure 0 And the average service life of the plunger pump obtained by accelerated test optimization
The relative percent error (RPD) was calculated, the RPD with the largest absolute value being the RPD under this test protocol:
step 07, repeating the steps 03 to 06 until the preset simulation times Z; taking the maximum value in the Z-time simulation scheme as the final RPD of the simulation in the scene, and then entering step 8;
step 08, repeating the steps 03 to 07 until the scene number is larger than p, and ending so as to obtain p RPDs corresponding to the experimental design scheme L,k 。
3. The energy-saving optimization method for the accelerated life test of the axial plunger pump according to claim 1, characterized in that: the step (3) adopts a multi-objective stochastic programming solving method, and the specific steps for optimizing the accelerated life test scheme are as follows:
step 09, RPD according to the multi-scenario target value under each variable combination L,k Fitting probability distribution to obtain the distributed parameters under each variable combination;
step 10, a threshold value of a specific objective function is given, RPDth, and the cumulative probability P (RPD is less than or equal to RPDth) meeting the threshold value under each variable combination is determined according to the parameters of fitting distribution;
and 11, sequencing all variable combinations according to the target function energy consumption E of the plunger pump constructed in the foregoing, obtaining the conditional probability of the multi-target optimal solution as each variable combination, and taking the expected value of one group or all the combinations with the highest probability as the final optimal solution.
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