A reliability analysis system and method for boom support of harvesting and breeding machine based on probability box

Abstract

The present application discloses a reliability analysis system and method for a harvesting machine arm frame based on a probability box, the system comprising: a variable acquisition unit, a model construction unit, a failure probability determination unit and a boundary calculation unit; the variable acquisition unit is used to obtain multiple uncertainty parameters of the harvesting machine arm frame, recorded as probability box variables; the model construction unit is used to construct a probability box model between the probability box variables and the response samples under the condition that multiple uncertainty parameters are independent of each other; the failure probability determination unit is used to determine the failure probability corresponding to the probability box model according to the upper and lower boundaries of the uncertainty parameters and the derivative of the cumulative distribution function of the uncertainty parameters; the boundary calculation unit is used to calculate the failure upper boundary and the failure lower boundary of the failure probability, so as to perform reliability analysis on the harvesting machine arm frame. Through the technical solution in the present application, the problems of failure of the harvesting machine arm frame under the influence of a small number of sample factors and waste caused by overly conservative design are solved.

Description

Technical Field

[0001] The present application relates to the technical field of a harvesting and breeding machine, and in particular, to a reliability analysis system for a harvesting and breeding machine arm based on a probability box and a reliability analysis method for a harvesting and breeding machine arm based on a probability box. Background Art

[0002] Combined harvesting and cultivation machines are widely used in the field of forestry engineering. Figure 1 As shown, the boom is the key operating component and main load-bearing component of the combined harvesting and breeding machine, and the safety of its structure determines the operating performance of the whole machine. The boom mainly includes the main arm and the auxiliary arm, and its working trajectory mainly depends on the mutual movement and coordination of the hydraulic cylinders of the working device. Therefore, from the perspective of traditional mechanical performance analysis, the force situation of the boom is complex, mainly bearing its own gravity, as well as the force or torque of the working device and hydraulic cylinder. The reliability index of the boom of the harvesting and breeding machine directly determines the service life of the whole machine. Therefore, it is necessary to provide key parameters for the overall design of the boom through reliability analysis.

[0003] At present, the reliability analysis of the combined harvesting machine boom is generally based on a probability model, and this method of reliability analysis using a probability model requires the construction of an accurate random distribution based on a large amount of uncertainty information. Although the uncertainty of some structural parameters in the harvesting machine boom can be described by an accurate random variable distribution, for some special parameters, such as the external working load of the harvesting machine, the main physical parameters of the material, the output pressure of the hydraulic cylinder, etc., due to the limitations of test costs, special tests that cannot be repeated many times, cognitive defects and other conditions, it is impossible to obtain enough test samples to construct the uncertainty variables of the probability density function or distribution function, and thus it is impossible to characterize it with an accurate probability distribution, and the reliability description can only be based on the upper and lower boundary values ​​defined by the experience of experts or technicians.

[0004] In the prior art, the combined harvesting and breeding machine arm frame designed according to this type of reliability analysis method has two problems during use:

[0005] On the one hand, for the parameters that determine the reliability of the combined harvesting machine, such as external working load, material elastic modulus, Poisson's ratio, hydraulic cylinder pressure oil output pressure, etc., it is impossible to obtain accurate probability distribution due to test costs or lack of knowledge, which leads to inaccurate reliability analysis of the traditional combined harvesting machine boom, resulting in a decrease in the quality of the combined harvesting machine as a whole;

[0006] On the other hand, due to the inaccurate reliability analysis of the combined harvesting and breeding machine boom, in order to avoid premature failure of the combined harvesting and breeding machine boom, overly conservative designs are often adopted in material selection and parameter matching during the boom design process, resulting in a waste of manufacturing costs. Summary of the invention

[0007] The purpose of this application is to improve the accuracy of reliability analysis of the boom of a harvesting and breeding machine, and to solve problems such as failure of the boom under the influence of a small number of sample factors and waste caused by overly conservative design.

[0008] The technical solution of the first aspect of the present application is: a probability box-based reliability analysis system for a harvesting machine arm is provided, the system comprising: a variable acquisition unit, a model construction unit, a failure probability determination unit and a boundary calculation unit; the variable acquisition unit is used to obtain multiple uncertainty parameters of the harvesting machine arm, recorded as probability box variables; the model construction unit is used to construct a probability box model between the probability box variables and the response samples under the condition that multiple uncertainty parameters are independent of each other; the failure probability determination unit is used to determine the failure probability corresponding to the probability box model according to the upper and lower boundaries of the uncertainty parameters and the derivative of the cumulative distribution function of the uncertainty parameters; the boundary calculation unit is used to calculate the upper failure boundary and the lower failure boundary of the failure probability, so as to perform reliability analysis on the harvesting machine arm.

[0009] In any of the above technical solutions, further, the uncertainty parameters at least include: the load on the boom of the harvesting and breeding machine, the deformation of the boom material and the working pressure of the boom cylinder;

[0010] The response sample shall at least include: lifting force of the lifting arm of the harvesting machine.

[0011] In any of the above technical solutions, further, the failure probability determination unit is configured as follows: Step 10, under the condition that multiple uncertainty parameters are independent of each other, select an uncertainty parameter in the probability box model as the intermediate operation uncertainty parameter, and set the values ​​of the remaining uncertainty parameters to preset values; Step 20, according to the upper and lower boundaries of the uncertainty parameters, calculate the average change of two adjacent parameters in the uncertainty parameters; Step 30, calculate the derivative of the cumulative distribution function of the intermediate operation uncertainty parameters to generate a joint probability density function; Step 40, according to the joint probability density function and the average change, transform the failure probability expression of the intermediate operation uncertainty parameter, and reselect the next uncertainty parameter, and execute step 10 until the transformed failure probability expressions of each uncertainty parameter are obtained; Step 50, according to the transformed failure probability expressions of the multiple uncertainty parameters, determine the failure probability corresponding to the probability box model.

[0012] In any of the above technical solutions, further, the joint probability density function is calculated by a differential method.

[0013] In any of the above technical solutions, further, the boundary calculation unit is used to calculate the upper failure boundary and the lower failure boundary of the failure probability, specifically comprising: step A, given the cumulative distribution of three uncertainty parameters Q1, Q2 and Q3, and respectively using and Indicates; Step B, using an iterative approach, based on the optimization strategy corresponding to the upper and lower boundary functions, find the probability function The three uncertainty parameters with the maximum values ​​are obtained to form the current boundary value; in step C, the boundary value gradient is calculated according to the current boundary value and the boundary value of the previous iteration, and it is determined whether the boundary value gradient is less than or equal to the preset error. If so, the current boundary value is used as the upper failure boundary and the lower failure boundary of the failure probability. Otherwise, step B is re-executed to perform the next iteration.

[0014] The technical solution of the second aspect of the present application is: a reliability analysis method for a harvesting machine arm based on a probability box is provided, the method comprising: step 1, obtaining multiple uncertainty parameters of the harvesting machine arm, recorded as probability box variables; step 2, constructing a probability box model between the probability box variables and the response samples under the condition that multiple uncertainty parameters are independent of each other; step 3, determining the failure probability corresponding to the probability box model according to the upper and lower boundaries of the uncertainty parameters and the derivative of the cumulative distribution function of the uncertainty parameters; step 4, calculating the upper failure boundary and the lower failure boundary of the failure probability to perform reliability analysis on the harvesting machine arm.

[0015] In any of the above technical solutions, further, the uncertainty parameters at least include: the load on the boom of the harvesting and breeding machine, the deformation of the boom material and the working pressure of the boom cylinder;

[0016] The response sample shall at least include: lifting force of the lifting arm of the harvesting machine.

[0017] In any of the above technical solutions, further, in step 3, it specifically includes: step 301, under the condition that multiple uncertainty parameters are independent of each other, select an uncertainty parameter in the probability box model as the intermediate operation uncertainty parameter, and set the values ​​of the remaining uncertainty parameters to preset values; step 302, calculate the derivative of the cumulative distribution function of the intermediate operation uncertainty parameter to generate a joint probability density function; step 303, calculate the average change of two adjacent parameters in the uncertainty parameter according to the upper and lower boundaries of the uncertainty parameter; step 304, transform the failure probability expression of the intermediate operation uncertainty parameter according to the joint probability density function and the average change, and reselect the next uncertainty parameter, execute step 301, until the transformed failure probability expression of each uncertainty parameter is obtained; step 305, determine the failure probability corresponding to the probability box model according to the transformed failure probability expressions of multiple uncertainty parameters.

[0018] In any of the above technical solutions, further, the joint probability density function is calculated by a differential method.

[0019] In any of the above technical solutions, further, in step 4, calculating the upper failure boundary and the lower failure boundary of the failure probability specifically includes: step 401, given the cumulative distribution of three uncertainty parameters Q1, Q2 and Q3, and using and In step 402, an iterative method is used to find the probability function based on the optimization strategy corresponding to the upper and lower boundary functions. The three uncertainty parameters with the maximum values ​​are obtained to form the current boundary value; in step 403, the boundary value gradient is calculated according to the current boundary value and the boundary value of the previous iteration, and it is determined whether the boundary value gradient is less than or equal to the preset error. If so, the current boundary value is used as the upper failure boundary and the lower failure boundary of the failure probability. Otherwise, step B is re-executed to perform the next iteration.

[0020] The beneficial effects of this application are:

[0021] The technical solution in the present application uses a probability box variable model to describe the uncertainty of the structure and operating parameters of the harvesting machine arm, so as to better deal with the deficiency of being unable to obtain accurate distribution due to small samples in actual engineering.

[0022] Afterwards, the mutual independence of uncertainty parameters is taken as a prerequisite, and the average change of two adjacent parameters in the uncertainty parameters and the joint probability density function of the uncertainty parameters are calculated respectively through the reliability analysis method based on probability box variables, and then the failure probability expression is transformed to obtain the failure probability corresponding to the probability box model, and then the corresponding upper and lower failure boundaries are obtained. Through the technical solution in this application, the failure boundary of the boom system of the harvesting and breeding machine can be efficiently obtained, the accuracy of the reliability analysis of the boom of the harvesting and breeding machine is improved, and the calculation cost is greatly reduced. The obtained failure probability boundary can provide an important reference for the design and use of the boom of the harvesting and breeding machine, avoiding failures under the influence of small sample factors, waste caused by overly conservative design, and other problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The advantages of the above and / or additional aspects of the present application will become apparent and easily understood in the description of the embodiments in conjunction with the following drawings, in which:

[0024] Figure 1 It is a schematic diagram of the structure of a harvesting and breeding machine in the prior art;

[0025] Figure 2 It is a schematic block diagram of a probability box-based boom reliability analysis system for a harvesting and breeding machine according to an embodiment of the present application;

[0026] Figure 3 This is a three-dimensional model diagram of a harvesting and breeding machine arm according to an embodiment of the present application;

[0027] FIG4( a) is a finite element model diagram of a main arm of a harvesting and breeding machine arm frame according to an embodiment of the present application;

[0028] FIG4( b ) is a finite element model diagram of a boom auxiliary arm of a harvesting and breeding machine according to an embodiment of the present application;

[0029] Figure 5 is a schematic diagram of a probability box according to an embodiment of the present application;

[0030] Figure 6 It is a schematic flow chart of a method for analyzing the reliability of a harvesting machine arm based on a probability box according to an embodiment of the present application. DETAILED DESCRIPTION

[0031] In order to more clearly understand the above-mentioned purposes, features and advantages of the present application, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0032] In the following description, many specific details are elaborated to facilitate a full understanding of the present application. However, the present application may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present application is not limited to the specific embodiments disclosed below.

[0033] Embodiment 1:

[0034] like Figure 2 As shown, this embodiment provides a probability box-based boom reliability analysis system 100 for a harvesting machine, comprising: a variable acquisition unit 10, a model building unit 20, a failure probability determination unit 30, and a boundary calculation unit 40; wherein the variable acquisition unit 10 is used to acquire multiple uncertainty parameters of the boom of the harvesting machine, recorded as probability box variables;

[0035] Specifically, taking the FB150-9P type harvesting and breeding machine as an example, the boom of the harvesting and breeding machine is simulated and modeled. Figure 3 As shown, corresponding sensors are set on the boom of the breeding machine, such as gravity sensors, strain gauge sensors, and pressure sensors, so as to sample uncertainty parameters such as the load on the boom of the breeding machine, the deformation of the boom material, and the working pressure of the boom cylinder as probability box variables and save them.

[0036] However, due to the cost of the test, it is impossible to do a large number of sampling tests. Therefore, this embodiment introduces the probability box principle and uses the variable acquisition unit 10 to obtain the above uncertainty parameters as probability box variables to obtain the boundaries of the probability density of the three variables themselves. Then, a model construction unit 20 is set in the system, and the model construction unit 20 is used to construct a probability box model between the probability box variable and the response sample under the condition that multiple uncertainty parameters are independent of each other;

[0037] Specifically, the finite element analysis unit is used to establish the finite element model of the main arm and auxiliary arm of the breeding machine boom, as shown in Figure 4(a) and Figure 4(b), and the established finite element model is meshed. The finite element mesh model of the breeding machine boom is set as the boundary condition, and the working target (response sample) of the breeding machine corresponding to the uncertainty parameters (probability box variables) such as the load, boom material deformation and boom cylinder working pressure is calculated: the lifting force of the breeding machine boom.

[0038] During the analysis process, the load on the boom of the mining machine, the deformation of the boom material (elastic modulus) and the working pressure of the boom cylinder are taken as input, and the lifting force of the boom of the mining machine is taken as response. The probability box variable set of uncertain parameters such as the load on the boom of the mining machine, the deformation of the boom material and the working pressure of the boom cylinder, as well as the response sample set of the lifting force are constructed.

[0039] This embodiment uses a probability box (P-box) model to characterize the uncertainty of the load on the boom of the breeding machine, the deformation of the boom material and the working pressure of the boom cylinder, and compares the lifting force of the boom of the breeding machine and its corresponding allowable value, and gives the upper and lower boundaries of the reliability index for measuring the reliability of the breeding machine boom, thereby reflecting the reliability of the breeding machine boom.

[0040] By sampling tests on the load on the boom of the harvesting machine, the deformation of the boom material and the working pressure of the boom cylinder, the probability box variable set of the input parameters is obtained, and the corresponding response sample set can be obtained through the probability box variable set.

[0041] Through the expert weighted scoring method, the probability distribution of the probability box variable and the response sample is described by a probability box with boundaries, as shown in the following formula:

[0042]

[0043] In the formula, Q = [Q1, Q2, Q3] represents the probability box variable composed of uncertainty parameters such as the load on the boom of the harvesting machine, the deformation of the boom material, and the working pressure of the boom cylinder. After the probability box variable is introduced to measure it, the probability distribution F of Q Q (q) is no longer an exact value, but a value bounded by the upper bound. Lower Boundary F Q(q) composed of intervals, such as Figure 5 shown.

[0044] Obviously, the value of the lifting force of the picker boom obtained by taking the probability box variable Q as input is definitely not a definite value, and its distribution is also a probability box.

[0045] The limit state equation of the picker boom system is established, where the input parameters are [S, Q]:

[0046] G=G(S,Q)=R(S,Q)-T(S,Q) (2)

[0047] Where R(·) is the resistance of the boom to deformation, T(·) is the stress generated by the load on the boom, and they are all functions of the input variables S and Q. S = [S1, S2, ...] is a random variable vector, representing other structural parameters or working condition parameters of the boom system, such as engine output power, working hours of a shift, and the number of boom lifts per working hour, etc., and its joint distribution type and distribution parameters are known; Q is a probability box variable random variable, representing the vector composed of three types of uncertainty parameters such as the load on the boom, the deformation of the boom material, and the working pressure of the boom cylinder, recorded as a probability box variable, and the distribution type and distribution parameter interval of each component are unknown, and it is represented here by a probability box variable model.

[0048] It should be noted that when G(S,Q)<0, that is, R(S,Q)<T(S,Q), the boom of the harvester fails; conversely, when R(S,Q)>T(S,Q), that is, G(S,Q)>0, the boom of the harvester is reliable.

[0049] According to the definition of reliability, the probability density function of the limit state equation of the harvesting machine arm is integrated in the failure domain to obtain its failure probability:

[0050] P f =∫ G(s,Q)≤0 f(G)dy

[0051] Where f(G) is the probability density function of the limit state equation G=G(S,Q)=R(S,Q)-T(S,Q), and G(S,Q)<0 is the failure domain of the boom of the harvesting machine.

[0052] Assuming that the random variable vector S and the probability box variable Q are statistically independent, the limit state equation of the picker arm is set as the integral domain. Therefore, the failure probability function of the picker arm can be given by the following formula:

[0053] P f =∫ G(s,Q)≤0 f Q (q)f s(s)dqds (3)

[0054] In the formula, f Q (q) is the joint probability density function of the probability box input variable vector Q of the harvesting machine arm, f S (s) is the joint probability density function of other random variable vectors S that affect the performance of the harvesting machine boom.

[0055] Assuming that the probability box variable Q takes a certain value q, that is, Q = q, its conditional probability ξ Q (q) can be expressed as:

[0056]

[0057] Assuming that the component variables in the probability box variable Q = [Q1, Q2, Q3] of the harvesting machine arm are independent of each other, the failure probability of the harvesting machine arm (Formula (3)) can be rewritten as:

[0058]

[0059] ξ Q (q) = ∫ G(S,Q＝q)≤0 f S (s)ds

[0060] Q={Q i}, i = 1, 2, 3

[0061] Q m = {q i},i=1,2,…,N

[0062] In the formula, Q is the probability box variable, Q i is the i-th uncertainty parameter in the probability box variable, q i is the uncertainty parameter Q i The i-th parameter in P f is the failure probability, ξ Q (q) is the conditional probability when the probability box variable is q parameter, is the joint probability density function corresponding to the probability box variable, f S (s) is the joint probability density function of the random variable vector s.

[0063] In this embodiment, the failure probability determination unit 30 is used to determine the failure probability corresponding to the probability box model according to the upper and lower boundaries of the uncertainty parameter and the derivative of the cumulative distribution function of the uncertainty parameter. The failure probability determination unit 30 is configured as follows:

[0064] Step 10, under the condition that multiple uncertainty parameters are independent of each other, select an uncertainty parameter in the probability box model as an intermediate operation uncertainty parameter, and set the values ​​of the remaining uncertainty parameters to preset values;

[0065] Step 20, calculating the average change of two adjacent parameters in the uncertainty parameter according to the upper and lower boundaries of the uncertainty parameter;

[0066] Specifically, taking a single uncertainty parameter Q as an example, we set its upper and lower bounds to be Q max and Q min , rewrite the failure probability expression of the harvesting machine (Formula (3)) into the following summation form:

[0067]

[0068] in,

[0069]

[0070] Where N represents the number of discrete points.

[0071] According to formula (7), the average change of two adjacent parameters in the uncertainty parameter can be obtained, that is:

[0072]

[0073] Step 30, calculating the derivative of the cumulative distribution function of the intermediate operation uncertainty parameter to generate a joint probability density function;

[0074] Specifically, the joint probability density function f related to one of the uncertainty parameters Q of the harvesting machine arm is Q (q) can be obtained by the cumulative distribution function F Q (q) is derived to obtain:

[0075]

[0076] In order to improve the joint probability density function f Q (q) is solved efficiently. This embodiment adopts a differential method to obtain the joint probability density function f related to a certain uncertainty parameter Q in the boom of the harvesting machine. Q (q (i) ), the corresponding calculation formula is:

[0077]

[0078] Step 40, transform the failure probability expression of the intermediate operation uncertainty parameter according to the joint probability density function (Formula 10) and the average change (Formula 8), and reselect the next uncertainty parameter and execute step 1 until the failure probability expression of each uncertainty parameter after transformation is obtained;

[0079] Specifically, by substituting formula (10) into formula (6), the failure probability of the boom of the harvesting machine can be further calculated by the following formula:

[0080]

[0081] Substituting formula (8) into formula (11), the transformed failure probability expression is:

[0082]

[0083] In addition, since the value of the discrete point number N is generally finite, the above formula can be approximated as:

[0084]

[0085] At the same time, formula (13) can be rewritten as:

[0086]

[0087] At this point, through the above conversion process, the failure probability problem of the boom of the harvesting and breeding machine containing uncertain parameter inputs is converted from the traditional high-dimensional integral form to the finite summation form at discrete points, and the difficulty of solving it is simplified.

[0088] At the same time, because the cumulative distribution F of the picker arm system Q is the uncertainty parameter Q in any It is obvious that F Q It has been discretized into N interval variables. At the same time, the failure probability P of the harvesting machine arm f It is no longer a single definite value in the traditional sense, it also becomes an interval value of a probability box:

[0089]

[0090] Since the distribution type and parameters of the probability box variable are unknown, F Q is to be solved. And the conditional probability ξ Q It is an exact probability random variable. Its value can be obtained by substituting discrete independent variable points into its expression, so it is known.

[0091] In this embodiment, the boundary calculation unit 40 is used to calculate the upper failure boundary and the lower failure boundary of the failure probability to perform reliability analysis on the boom of the harvesting and breeding machine.

[0092] Specifically, formula (14) shows that the failure probability P f is just a function with the cumulative distribution F Q The linear expression related to this is the upper bound of the failure probability of the picker arm. and the lower boundary P fIt can be obtained by solving the following two optimization problems, and the corresponding functions are:

[0093]

[0094] and

[0095]

[0096] From equations (16) to (17), we can see that once the conditional probability ξ Q After the determination, the above linear programming model can be solved by simplex method and other methods, so as to conveniently obtain the cumulative distribution F of the picker arm Q and the interval of failure probability

[0097] It should be noted that the above formula (13) can only be used to calculate the failure probability of one probability box variable (uncertainty parameter). Therefore, when calculating the upper and lower failure boundaries of the failure probability, first use one uncertainty parameter as a variable and the rest as fixed values. Each time, only the failure probability of one probability box variable is calculated. After that, the failure probability of the next probability box variable is calculated after it is fixed, and so on, until the failure probability of all probability box variables is obtained. At this time, the minimum or maximum failure probability is its boundary.

[0098] Furthermore, the boundary calculation unit 40 is used to calculate the upper failure boundary and the lower failure boundary of the failure probability, specifically including:

[0099] Step A, given the cumulative distribution of three uncertainty parameters Q1, Q2 and Q3, and using and express;

[0100] Step B, using an iterative approach, based on the optimization strategies corresponding to the upper and lower boundary functions, sequentially find the probability function Get the three uncertainty parameters with the maximum value to form the current boundary value;

[0101] Step C, calculate the boundary value gradient according to the current boundary value and the boundary value of the previous iteration, and determine whether the boundary value gradient is less than or equal to the preset error. If so, use the current boundary value as the upper failure boundary and the lower failure boundary of the failure probability. Otherwise, re-execute step B and perform the next iteration.

[0102] Specifically, for the failure probability P of the three uncertain parameter input variables including the load on the boom of the harvesting machine, the deformation of the boom material and the working pressure of the boom cylinder, f , can be viewed as a function with three uncertainty parameters as independent variables:

[0103]

[0104] Where h() is a probability function of a 3D uncertainty parameter variable, for The abbreviation of .

[0105] The upper limit of failure probability Taking as an example, the optimization process of failure probability boundary is carried out as follows:

[0106] Step 1. Given the cumulative distribution of input uncertainty parameters Q1, Q2 and Q3, and using and Indicates; set the preset error ε, st = 0, and

[0107] Step 2. Use the optimization strategy corresponding to the upper boundary function to find the probability function based on the determined last two uncertainty parameters. The largest first uncertainty parameter Next, based on the determined first and third uncertainty parameters, we look for the probability function Get the second uncertainty parameter with the maximum value Next, based on the determined first and second uncertainty parameters, find a method that can make the probability function The third uncertainty parameter with the maximum value At this point, the current boundary value can be formed

[0108] Step 3. If the boundary value gradient Let st = st + 1, and go to the second step; otherwise, take st+ 1P f As the upper limit of failure probability

[0109] For 3 probability box variables, and only the upper boundary of the failure boundary Take the case of an example. Since the failure probability of the picker arm can be rewritten as:

[0110]

[0111] It can also be written as:

[0112]

[0113] Assume that q2 is fixed first to find the probability of failure (probability function) P f The largest uncertainty parameters are q1 and q3. At this time, the conditional probability ξ Q (q) can be written as:

[0114]

[0115] Substituting formula (21) into formula (20), the failure probability of the boom of the harvesting machine can be obtained:

[0116]

[0117] At this point, the original multivariable problem has been converted into a single variable problem, which can be solved using the proposed solution strategy. Equation (21) can be obtained using the first order reliability method (FORM), and the upper bound of the failure probability of the harvesting machine boom can be obtained using the optimization model for the uncertainty parameter q1. The corresponding calculation formula is:

[0118]

[0119] Similarly, after the uncertainty parameters q1 and q3 are obtained and fixed, a similar optimization model can be used to obtain the failure probability P under the above conditions. f Maximize the uncertainty parameter q2:

[0120]

[0121] Similarly, after the uncertainty parameters q1 and q2 are obtained and fixed, a similar optimization model can be used to obtain the failure probability P under the above conditions. f Maximize the uncertainty parameter q3:

[0122]

[0123] At this time, the desired This is the upper limit of the final failure probability required Similarly, the lower bound of the failure probability is P f It can also be obtained using the above method, as long as the maximization optimization model is changed to a minimization optimization model. The specific process will not be repeated here.

[0124] Embodiment 2:

[0125] like Figure 6 As shown, this embodiment provides a method for analyzing the reliability of a harvesting machine arm frame based on a probability box, including:

[0126] Step 1, obtaining multiple uncertainty parameters of the boom of the harvesting machine and recording them as probability box variables;

[0127] Specifically, taking the FB150-9P type harvesting and breeding machine as an example, the boom of the harvesting and breeding machine is simulated and modeled. Figure 3As shown, corresponding sensors are set on the boom of the breeding machine, such as gravity sensors, strain gauge sensors, and pressure sensors, so as to sample uncertainty parameters such as the load on the boom of the breeding machine, the deformation of the boom material, and the working pressure of the boom cylinder as probability box variables and save them.

[0128] Step 2, construct a probability box model between probability box variables and response samples under the condition that multiple uncertainty parameters are independent of each other; wherein the uncertainty parameters include at least: the load on the boom of the harvesting machine, the deformation of the boom material and the working pressure of the boom cylinder; the response samples include at least: the lifting force of the boom of the harvesting machine.

[0129] Specifically, due to the cost of the test, it is impossible to do a large number of sampling tests. Therefore, this embodiment introduces the probability box principle and uses the above uncertainty parameters as probability box variables to obtain the boundaries of the probability density of the three variables themselves.

[0130] The finite element analysis unit is used to establish the finite element model of the main arm and auxiliary arm of the breeding machine boom, as shown in Figure 4(a) and Figure 4(b), and the established finite element model is meshed. The finite element mesh model of the breeding machine boom is set as the boundary condition, and the working target (response sample) of the breeding machine corresponding to the uncertainty parameters (probability box variables) such as the load, boom material deformation and boom cylinder working pressure is calculated: the lifting force of the breeding machine boom.

[0131] During the analysis process, the load on the boom of the mining machine, the deformation of the boom material (elastic modulus) and the working pressure of the boom cylinder are taken as input, and the lifting force of the boom of the mining machine is taken as response. The probability box variable set of uncertain parameters such as the load on the boom of the mining machine, the deformation of the boom material and the working pressure of the boom cylinder, as well as the response sample set of the lifting force are constructed.

[0132] This embodiment uses a probability box (P-box) model to characterize the uncertainty of the load on the boom of the breeding machine, the deformation of the boom material and the working pressure of the boom cylinder, and compares the lifting force of the boom of the breeding machine and its corresponding allowable value, and gives the upper and lower boundaries of the reliability index for measuring the reliability of the breeding machine boom, thereby reflecting the reliability of the breeding machine boom.

[0133] By sampling tests on the load on the boom of the harvesting machine, the deformation of the boom material and the working pressure of the boom cylinder, the probability box variable set of the input parameters is obtained, and the corresponding response sample set can be obtained through the probability box variable set.

[0134] Through the expert weighted scoring method, the probability distribution of the probability box variable and the response sample is described by a probability box with boundaries, as shown in the following formula:

[0135]

[0136] In the formula, Q = [Q1, Q2, Q3] represents the probability box variable composed of uncertainty parameters such as the load on the boom of the harvesting machine, the deformation of the boom material, and the working pressure of the boom cylinder. After the probability box variable is introduced to measure it, the probability distribution F of Q Q (q) is no longer an exact value, but a value bounded by the upper bound. Lower Boundary F Q (q) composed of intervals, such as Figure 5 shown.

[0137] Obviously, the value of the lifting force of the picker boom obtained by taking the probability box variable Q as input is definitely not a definite value, and its distribution is also a probability box.

[0138] The limit state equation of the picker boom system is established, where the input parameters are [S, Q]:

[0139] G=G(S,Q)=R(S,Q)-T(S,Q) (2)

[0140] Where R(·) is the resistance of the boom to deformation, T(·) is the stress generated by the load on the boom, and they are all functions of the input variables S and Q. S = [S1, S2, ...] is a random variable vector, representing other structural parameters or working condition parameters of the boom system, such as engine output power, working hours of a shift, and the number of boom lifts per working hour, etc., and its joint distribution type and distribution parameters are known; Q is a probability box variable random variable, representing the vector composed of three types of uncertainty parameters such as the load on the boom, the deformation of the boom material, and the working pressure of the boom cylinder, recorded as a probability box variable, and the distribution type and distribution parameter interval of each component are unknown, and it is represented here by a probability box variable model.

[0141] It should be noted that when G(S,Q)<0, that is, R(S,Q)<T(S,Q), the boom of the harvester fails; conversely, when R(S,Q)>T(S,Q), that is, G(S,Q)>0, the boom of the harvester is reliable.

[0142] According to the definition of reliability, the probability density function of the limit state equation of the harvesting machine arm is integrated in the failure domain to obtain its failure probability:

[0143] P f =∫ G(S,Q)≤0 f(G)dy

[0144] Where f(G) is the probability density function of the limit state equation G=G(S,Q)=R(S,Q)-T(S,Q), and G(S,Q)<0 is the failure domain of the boom of the harvesting machine.

[0145] Assuming that the random variable vector S and the probability box variable Q are statistically independent, the limit state equation of the picker arm is set as the integral domain. Therefore, the failure probability function of the picker arm can be given by the following formula:

[0146] P f =∫ G(S,Q)≤0 f Q (q)f S (s)dqds (3)

[0147] In the formula, f Q (q) is the joint probability density function of the probability box input variable vector Q of the harvesting machine arm, f S (s) is the joint probability density function of other random variable vectors S that affect the performance of the harvesting machine boom.

[0148] Assuming that the probability box variable Q takes a certain value q, that is, Q = q, its conditional probability ξ Q (q) can be expressed as:

[0149]

[0150] Assuming that the component variables in the probability box variable Q = [Q1, Q2, Q3] of the harvesting machine arm are independent of each other, the failure probability of the harvesting machine arm (Formula (3)) can be rewritten as:

[0151]

[0152] ξ Q (q) = ∫ G(s,Q＝q)≤0 f S (s)ds

[0153] Q={Q i}, i = 1, 2, 3

[0154] Q m = {q i},i=1,2,…,N

[0155] In the formula, Q is the probability box variable, Q i is the i-th uncertainty parameter in the probability box variable, q i is the uncertainty parameter Q i The i-th parameter in P f is the failure probability, ξ Q (q) is the conditional probability when the probability box variable is q parameter, is the joint probability density function corresponding to the probability box variable, f S (s) is the joint probability density function of the random variable vector s.

[0156] Step 3, determining the failure probability corresponding to the probability box model according to the upper and lower bounds of the uncertainty parameter and the derivative of the cumulative distribution function of the uncertainty parameter;

[0157] Furthermore, step 3 specifically includes:

[0158] Step 301, under the condition that multiple uncertainty parameters are independent of each other, an uncertainty parameter in the probability box model is selected as an intermediate operation uncertainty parameter, and the values ​​of the remaining uncertainty parameters are set as preset values;

[0159] Step 302, calculate the derivative of the cumulative distribution function of the intermediate operation uncertainty parameter to generate a joint probability density function; wherein the joint probability density function is calculated by a differential method.

[0160] Specifically, taking a single uncertainty parameter Q as an example, we set its upper and lower bounds to be Q max and Q min , rewrite the failure probability expression of the harvesting machine (Formula (3)) into the following summation form:

[0161]

[0162] in,

[0163]

[0164] Where N represents the number of discrete points.

[0165] According to formula (7), the average change of two adjacent parameters in the uncertainty parameter can be obtained, that is:

[0166]

[0167] Step 303, calculating the average change of two adjacent parameters in the uncertainty parameter according to the upper and lower boundaries of the uncertainty parameter;

[0168] Specifically, the joint probability density function f related to one of the uncertainty parameters Q of the harvesting machine arm is Q (q) can be obtained by the cumulative distribution function F Q (q) is derived to obtain:

[0169]

[0170] In order to improve the joint probability density function f Q (q) is solved efficiently. This embodiment adopts a differential method to obtain the joint probability density function f related to a certain uncertainty parameter Q in the boom of the harvesting machine. Q (q (i) ), the corresponding calculation formula is:

[0171]

[0172] Step 304, transforming the failure probability expression of the intermediate operation uncertainty parameter according to the joint probability density function and the average change, and reselecting the next uncertainty parameter, and executing step 301 until the failure probability expression after the transformation of each uncertainty parameter is obtained;

[0173] Step 305: Determine the failure probability corresponding to the probability box model according to the transformed failure probability expressions of the multiple uncertainty parameters.

[0174] Specifically, by substituting formula (10) into formula (6), the failure probability of the boom of the harvesting machine can be further calculated by the following formula:

[0175]

[0176] Substituting formula (8) into formula (11), the transformed failure probability expression is:

[0177]

[0178] In addition, since the value of the discrete point number N is generally finite, the above formula can be approximated as:

[0179]

[0180] At the same time, formula (13) can be rewritten as:

[0181]

[0182] At this point, through the above conversion process, the failure probability problem of the boom of the breeding machine containing uncertain parameter input is converted from the traditional high-dimensional integral form to the finite summation form at discrete points, and the difficulty of solving it is simplified.

[0183] At the same time, because the cumulative distribution F of the picker arm system Q is the uncertainty parameter Q in any It is obvious that F Q It has been discretized into N interval variables. At the same time, the failure probability P of the picker arm f It is no longer a single definite value in the traditional sense, it also becomes an interval value of a probability box:

[0184]

[0185] Since the distribution type and parameters of the probability box variable are unknown, F Q is to be solved. And the conditional probability ξ QIt is an exact probability random variable. Its value can be obtained by substituting discrete independent variable points into its expression, so it is known.

[0186] Step 4, calculate the upper failure boundary and the lower failure boundary of the failure probability to conduct reliability analysis on the boom of the harvesting and breeding machine.

[0187] Specifically, formula (14) shows that the failure probability P f is just a function with the cumulative distribution F Q The linear expression related to this is the upper bound of the failure probability of the picker arm. and the lower boundary P f It can be obtained by solving the following two optimization problems, and the corresponding functions are:

[0188]

[0189] and

[0190]

[0191] From equations (16) to (17), we can see that once the conditional probability ξ Q After the determination, the above linear programming model can be solved by simplex method and other methods, so as to conveniently obtain the cumulative distribution F of the picker arm Q and the interval of failure probability

[0192] It should be noted that the above formula (13) can only be used to calculate the failure probability of one probability box variable (uncertainty parameter). Therefore, when calculating the upper and lower failure boundaries of the failure probability, first use one uncertainty parameter as a variable and the rest as fixed values. Each time, only the failure probability of one probability box variable is calculated. After that, the failure probability of the next probability box variable is calculated after it is fixed, and so on, until the failure probability of all probability box variables is obtained. At this time, the minimum or maximum failure probability is its boundary.

[0193] Furthermore, in step 4, the upper failure boundary and the lower failure boundary of the failure probability are calculated, specifically including:

[0194] Step 401, given the cumulative distribution of three uncertainty parameters Q1, Q2 and Q3, and using and express;

[0195] Step 402, using an iterative method, based on the optimization strategy corresponding to the upper and lower boundary functions, sequentially find the probability function Get the three uncertainty parameters with the maximum value to form the current boundary value;

[0196] Step 403, calculate the boundary value gradient according to the current boundary value and the boundary value of the previous iteration, and determine whether the boundary value gradient is less than or equal to the preset error. If so, use the current boundary value as the upper failure boundary and the lower failure boundary of the failure probability. Otherwise, re-execute step B and perform the next iteration.

[0197] Specifically, for the failure probability P of the three uncertain parameter input variables including the load on the boom of the harvesting machine, the deformation of the boom material and the working pressure of the boom cylinder, f , can be viewed as a function with three uncertainty parameters as independent variables:

[0198]

[0199] Where h() is a probability function of a 3D uncertainty parameter variable, for The abbreviation of .

[0200] The upper limit of failure probability Taking as an example, the optimization process of failure probability boundary is carried out as follows:

[0201] Step 1. Given the cumulative distribution of input uncertainty parameters Q1, Q2 and Q3, and using and Indicates; set the preset error ε, st = 0, and

[0202] Step 2. Use the optimization strategy corresponding to the upper boundary function to find the probability function based on the determined last two uncertainty parameters. The largest first uncertainty parameter Next, based on the determined first and third uncertainty parameters, we look for the probability function Get the second uncertainty parameter with the maximum value Next, based on the determined first and second uncertainty parameters, find a method that can make the probability function The third uncertainty parameter with the maximum value At this point, the current boundary value can be formed

[0203] Step 3. If the boundary value gradient Let st = st + 1, and go to the second step; otherwise, take st+ 1P f As the upper limit of failure probability

[0204] For 3 probability box variables, and only the upper boundary of the failure boundary Take the case of an example. Since the failure probability of the picker arm can be rewritten as:

[0205]

[0206] It can also be written as:

[0207]

[0208] Assume that q2 is fixed first to find the probability of failure (probability function) P f The largest uncertainty parameters are q1 and q3. At this time, the conditional probability ξ Q (q) can be written as:

[0209]

[0210] Substituting formula (21) into formula (20), the failure probability of the boom of the harvesting machine can be obtained:

[0211]

[0212] At this point, the original multivariable problem has been converted into a single variable problem, which can be solved using the proposed solution strategy. Equation (21) can be obtained using the first order reliability method (FORM), and the upper bound of the failure probability of the harvesting machine boom can be obtained using the optimization model for the uncertainty parameter q1. The corresponding calculation formula is:

[0213]

[0214] Similarly, after the uncertainty parameters q1 and q3 are obtained and fixed, a similar optimization model can be used to obtain the failure probability P under the above conditions. f Maximize the uncertainty parameter q2:

[0215]

[0216] Similarly, after the uncertainty parameters q1 and q2 are obtained and fixed, a similar optimization model can be used to obtain the failure probability P under the above conditions. f Maximize the uncertainty parameter q3:

[0217]

[0218] At this time, the desired This is the upper limit of the final failure probability required Similarly, the lower bound of the failure probability is P fIt can also be obtained using the above method, as long as the maximization optimization model is changed to a minimization optimization model. The specific process will not be repeated here.

[0219] The above describes the technical solution of the present application in detail in combination with the accompanying drawings. The present application proposes a reliability analysis system and method for a harvesting and breeding machine arm based on a probability box.

[0220] The system includes: a variable acquisition unit, a model construction unit, a failure probability determination unit and a boundary calculation unit; the variable acquisition unit is used to obtain multiple uncertainty parameters of the harvesting machine arm frame, recorded as probability box variables; the model construction unit is used to construct a probability box model between the probability box variables and the response sample under the condition that multiple uncertainty parameters are independent of each other; the failure probability determination unit is used to determine the failure probability corresponding to the probability box model according to the upper and lower boundaries of the uncertainty parameters and the derivative of the cumulative distribution function of the uncertainty parameters; the boundary calculation unit is used to calculate the upper and lower boundaries of the failure probability to perform reliability analysis on the harvesting machine arm frame. Through the technical solution in this application, the problems of failure of the harvesting machine arm frame under the influence of a small number of sample factors and waste caused by overly conservative design are solved.

[0221] The steps in this application can be adjusted in order, combined, and deleted according to actual needs.

[0222] The units in the device of the present application can be combined, divided and deleted according to actual needs.

[0223] Although the present application is disclosed in detail with reference to the accompanying drawings, it should be understood that these descriptions are merely exemplary and are not intended to limit the application of the present application. The scope of protection of the present application is defined by the appended claims and may include various modifications, alterations and equivalents made to the invention without departing from the scope and spirit of the present application.

Claims

1. A probability box-based boom reliability analysis system, characterized in that: The system includes: a variable acquisition unit, a model building unit, a failure probability determination unit and a boundary calculation unit; The variable acquisition unit is used to acquire multiple uncertainty parameters of the harvesting and breeding machine arm frame, which are recorded as probability box variables; The model building unit is used to build a probability box model between the probability box variables and the response samples under the condition that the multiple uncertainty parameters are independent of each other; The failure probability determination unit is used to determine the failure probability corresponding to the probability box model according to the upper and lower boundaries of the uncertainty parameter and the derivative of the cumulative distribution function of the uncertainty parameter; The boundary calculation unit is used to calculate the upper failure boundary and the lower failure boundary of the failure probability, so as to perform reliability analysis on the boom of the harvesting and breeding machine; The failure probability determination unit is configured to: Step 10, under the condition that the plurality of uncertainty parameters are independent of each other, selecting an uncertainty parameter in the probability box model as an intermediate operation uncertainty parameter, and setting the values ​​of the remaining uncertainty parameters as preset values; Step 20, calculating the average change of two adjacent parameters in the uncertainty parameter according to the upper and lower boundaries of the uncertainty parameter; Step 30, calculating the derivative of the cumulative distribution function of the intermediate operation uncertainty parameter to generate a joint probability density function; Step 40, transforming the failure probability expression of the intermediate operation uncertainty parameter according to the joint probability density function and the average variation, and reselecting the next uncertainty parameter, and executing step 10 until the failure probability expression of each uncertainty parameter after transformation is obtained; Step 50, determining the failure probability corresponding to the probability box model according to the transformed failure probability expressions of the multiple uncertainty parameters; The boundary calculation unit is used to calculate the upper failure boundary and the lower failure boundary of the failure probability, specifically including: Step A, given the cumulative distribution of three uncertainty parameters Q1, Q2 and Q3, and using 0F Q1 ,0F Q2 and 0F Q3 express; Step B, using an iterative approach, based on the optimization strategies corresponding to the upper and lower boundary functions, sequentially find the probability function h( st F Q1 , st F Q2 , st F Q3 ) obtain the three uncertainty parameters with the maximum value to form the current boundary value; Step C, calculate the boundary value gradient according to the current boundary value and the boundary value of the previous iteration, and determine whether the boundary value gradient is less than or equal to the preset error. If so, use the current boundary value as the upper failure boundary and the lower failure boundary of the failure probability. Otherwise, re-execute step B and perform the next iteration.

2. The probability box-based reliability analysis system for the harvesting and breeding machine arm support according to claim 1, characterized in that: The uncertainty parameters include at least: the load on the boom of the harvesting machine, the deformation of the boom material and the working pressure of the boom cylinder; The response sample at least includes: the lifting force of the lifting arm of the harvesting and breeding machine.

3. The probability box-based reliability analysis system for the harvesting and breeding machine arm frame according to claim 1, characterized in that: The joint probability density function is calculated by difference.

4. A reliability analysis method for a harvesting machine arm based on a probability box, characterized in that: The method includes: Step 1, obtaining multiple uncertainty parameters of the boom of the harvesting machine and recording them as probability box variables; Step 2, constructing a probability box model between the probability box variables and the response samples under the condition that the multiple uncertainty parameters are independent of each other; Step 3, determining the failure probability corresponding to the probability box model according to the upper and lower boundaries of the uncertainty parameter and the derivative of the cumulative distribution function of the uncertainty parameter; Step 4, calculating the upper failure boundary and the lower failure boundary of the failure probability to perform reliability analysis on the boom of the harvesting and breeding machine; The step 3 specifically includes: Step 301, under the condition that the plurality of uncertainty parameters are independent of each other, an uncertainty parameter in the probability box model is selected as an intermediate operation uncertainty parameter, and the values ​​of the remaining uncertainty parameters are set as preset values; Step 302, calculating the derivative of the cumulative distribution function of the intermediate operation uncertainty parameter to generate a joint probability density function; Step 303, calculating the average change of two adjacent parameters in the uncertainty parameter according to the upper and lower boundaries of the uncertainty parameter; Step 304, transforming the failure probability expression of the intermediate operation uncertainty parameter according to the joint probability density function and the average variation, and reselecting the next uncertainty parameter, and executing step 301 until the failure probability expression after the transformation of each uncertainty parameter is obtained; Step 305, determining the failure probability corresponding to the probability box model according to the transformed failure probability expressions of the multiple uncertainty parameters; In step 4, calculating the upper failure boundary and the lower failure boundary of the failure probability specifically includes: Step 401, given the cumulative distribution of three uncertainty parameters Q1, Q2 and Q3, and using 0F Q1 ,0F Q2 and 0F Q3 express; Step 402, using an iterative method, based on the optimization strategies corresponding to the upper and lower boundary functions, sequentially find the probability function h( st F Q1 , st F Q2 , st F Q3 ) obtain the three uncertainty parameters with the maximum value to form the current boundary value; Step 403, calculate the boundary value gradient according to the current boundary value and the boundary value of the previous iteration, and determine whether the boundary value gradient is less than or equal to the preset error. If so, use the current boundary value as the upper failure boundary and the lower failure boundary of the failure probability. Otherwise, re-execute step 402 to perform the next iteration.

5. The reliability analysis method of the boom support of the harvesting and breeding machine based on probability box as claimed in claim 4 is characterized in that: The uncertainty parameters include at least: the load on the boom of the harvesting machine, the deformation of the boom material and the working pressure of the boom cylinder; The response sample at least includes: the lifting force of the lifting arm of the harvesting and breeding machine.

6. The reliability analysis method of the boom support of the harvesting and breeding machine based on probability box as claimed in claim 4 is characterized in that: The joint probability density function is calculated by difference.

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