Split zone test method and system based on association and randomization double limitation

Abstract

The invention discloses a crack zone test method and system based on association and randomization double limitation. According to the split zone test design analysis method, the influence of each factor on the result of the association and randomization double-limited task is accurately determined by rapidly eliminating interference factors. And the economical efficiency and sufficiency (cost-effectiveness ratio) of the test are improved. And professional testers are supported to make a more correct test scheme in a shorter time. By taking the success rate of the unmanned aerial vehicle search task as an example, key test factors are quickly found through a split area test design method, and the success rate of the unmanned aerial vehicle search task is improved. And meanwhile, a solid foundation is laid for supporting and developing a future task-oriented complex system / system simulation test.

Description

Technical Field

[0001] This invention relates to the field of split-plot experimental design, and specifically to a split-plot experimental method and system based on dual constraints of correlation and randomization. Background Technology

[0002] Experimental design methods, by scientifically manipulating the levels of controllable factors (independent variables) and systematically observing their impact on response variables (dependent variables), have wide applications in industrial production, engineering optimization, and scientific research. Common methods include full factorial design, partial factorial design, response surface methodology, robust parametric design, mixture design, uniform design, and optimal design, which provide fundamental tools for modeling and optimizing multi-factor systems in different scenarios. However, traditional experimental methods typically rely on a series of idealized statistical assumptions, such as complete randomization of the experimental sequence, design orthogonality, and factor independence, to ensure the validity and unbiasedness of statistical inference. Real-world experimental processes are often limited by equipment, cost, process, or safety conditions, making complete randomization of the experimental sequence impossible. This results in significant sequence constraints in most practical experiments, directly challenging the applicability of classical experimental theory.

[0003] Although randomization is a fundamental principle of experimental design, it is often difficult to strictly implement in engineering practice. This phenomenon is mainly reflected in the following two situations: In block design, when the experiment cannot be completed under uniform conditions, it is necessary to divide the experimental unit into several blocks according to its characteristics, with the goal of minimizing intra-block differences and maximizing inter-block differences. In this case, randomization can only be carried out within the blocks. In split-block design, due to the difficulty or high cost of adjusting some factor levels, it is necessary to arrange the difficult-to-change factors (HTC, such as process parameters such as temperature and pressure) in the whole block and the easily changeable factors (ETC, such as raw material ratio and operating speed) in the sub-block. Therefore, only partial randomization can be achieved, and the whole block is often subject to sequence restrictions.

[0004] Besides randomization constraints, the problem of inter-factor correlation constraints is another common and crucial limitation in engineering experiments. This phenomenon mainly refers to the fact that the level of a factor is not independent, but depends on the levels of one or more other factors. Such constraints usually stem from physical laws, equipment safety limits, or process feasibility requirements. For example, in the heat treatment process of high-strength materials, there is a strict correlation constraint between "quenching temperature" and "cooling rate." An excessively high cooling rate combined with an excessively high quenching temperature can easily lead to cracking of the parts. Therefore, the feasible combination of the two levels constitutes a non-rectangular, irregular region. Unlike the classic factor space (a hypercube with independent dimensions), the feasible region of such experiments with correlation constraints is often cut into complex polyhedra or non-convex spaces. This means that traditional full-factor designs or partial-factor designs may contain a large number of infeasible or dangerous test points, thus directly failing.

[0005] Split-plot design, as an efficient multi-factor experimental strategy, optimizes resource allocation and improves information acquisition efficiency by differentiating factors of varying importance and adjustment frequencies. In practice, each block is first divided into several main blocks (whole blocks) based on the number of levels of the main treatment (usually a factor difficult to change randomly), and the main treatment is randomly assigned to each main block. Then, each main block is further subdivided into smaller split-plots (sub-blocks) to accommodate the levels of sub-treatments (factors that are easily changed). From the perspective of the sub-treatments, each main block can be considered an independent block; however, from the perspective of the overall factor structure, the main blocks are incomplete blocks. This design, by differentiating the configuration of different factors, achieves more accurate estimations of various effects, significantly saving experimental resources and costs while improving information quality. It is particularly suitable for complex industrial environments where correlation and randomization are both constrained.

[0006] Based on the strength of the correlation between the main treatment levels and the required model complexity, split-plot experiments can be further subdivided into first-order and second-order correlation split-plot methods. Both are suitable for situations where the main treatment levels cannot be completely randomized and trend correlations exist, enabling the analysis of linear or quadratic trends in the main treatments and their interactions with secondary treatments. First-order methods are simple in structure and easy to implement, suitable for linear response systems; however, in engineering practice, systems often exhibit significant nonlinearity due to multi-factor coupling, making it difficult for first-order models to accurately describe the real process and potentially leading to misleading conclusions. Second-order correlation split-plot methods, by introducing higher-order terms and interaction effects, effectively capture nonlinear response characteristics, significantly improving the model's realism, predictive robustness, and engineering interpretability.

[0007] The dual constraints of randomization and association have become a critical constraint that cannot be ignored in modern experimental design, seriously affecting the validity of some assumptions in traditional experimental problems. Therefore, how to extract more effective information from the dual constraints of randomization and association with fewer trials, while ensuring the accuracy and reliability of model estimation, is a core problem that urgently needs to be solved in the field of experimental optimization. Summary of the Invention

[0008] To address the technical problems mentioned above, this invention proposes a split-plot experiment method based on dual constraints of correlation and randomization. This method systematically handles the actual situation of incomplete randomization and factors not being able to take independent values. Through structural optimization and innovative modeling strategies, it provides a systematic and practical solution for the efficient design and analysis of experiments in complex engineering environments.

[0009] To achieve the above objectives, this invention provides a split-plot experiment method based on dual constraints of correlation and randomization, comprising the following steps:

[0010] S1. Define the response variables and several experimental factors according to the experimental objective, and determine the value level of each experimental factor;

[0011] S2. Based on the value level of each experimental factor, construct the experimental design matrix according to the standard surface center design;

[0012] S3. Optimize the constructed experimental design matrix to obtain the optimized combination of experimental parameters;

[0013] S4. Arrange experiments according to the optimized combination of experimental parameters, collect experimental data and calculate variance;

[0014] S5. Based on the collected experimental data and calculated variance, fit the curve to establish a prediction model; and optimize the next experiment based on the prediction model.

[0015] Preferably, the experimental factors include: a principal region factor and a sliding factor, wherein the principal region factor is a difficult-to-change factor and the sliding factor is a easily changeable factor.

[0016] Preferably, in step S2, the method for constructing the experimental design matrix according to the standard plane center design includes: generating a two-dimensional matrix, where each row represents an experimental point and each column represents a factor, and determining the number of experimental points according to the design requirements.

[0017] Preferably, in step S3, the experimental design matrix is ​​optimized by calculating the codes of each experimental factor within its corresponding sliding region. The method for calculating the codes includes:

[0018]

[0019] in, It is the encoded value of the sliding factor at point i when the main region factor A is at level j; This refers to the original value of the sliding factor at point i when the principal region factor A is at level j. It represents the original value of the sliding factor at the center point when the principal region factor A is at level j, and Δ represents the radius of change of the sliding factor.

[0020]

[0021] in, and These represent the maximum and minimum values ​​of the sliding factor within the feasible experimental region when the main region factor A is at level j, respectively.

[0022] Preferably, in step S5, the step of calculating the variance includes:

[0023] Based on the principal and split-plot factors defined in the experimental design, determine the sources of variation in the analysis of variance;

[0024] Based on the identified sources of variation, calculate the degrees of freedom and sum of squares for each source of variation;

[0025] Based on the calculated degrees of freedom and sum of squares, estimates of the variance components corresponding to each source of variation are calculated.

[0026] Preferably, in step S5, the method for establishing a prediction model by fitting the curve includes:

[0027]

[0028] Where y represents the N×1 response vector; X represents the N×p fitting model matrix; β represents the p×1 fitting coefficient vector; σ represents the N×1 splitting error vector; N represents the total number of trials; and p represents the terms included in the fitting model.

[0029] Preferably, using the covariance matrix for parameter estimation improves the accuracy and reliability of the prediction model.

[0030] The expression for the covariance matrix E is as follows:

[0031]

[0032] in, This represents the squared error term of the cracked region; I represents the squared error term of the principal region; J represents the identity matrix; b This represents a block diagonal matrix.

[0033] The present invention also provides a split-plot test system based on dual constraints of correlation and randomization. The system is used to implement the above method and includes: a definition module, a design module, an optimization module, a calculation module, and a construction module.

[0034] The definition module is used to define response variables and several experimental factors according to the experimental purpose, and to determine the value level of each experimental factor;

[0035] The design module is used to construct an experimental design matrix according to the value level of each experimental factor and the standard surface center design.

[0036] The optimization module is used to optimize the constructed experimental design matrix to obtain an optimized combination of experimental parameters;

[0037] The calculation module is used to arrange experiments according to the optimized combination of experimental parameters, collect experimental data, and calculate variance.

[0038] The building module is used to fit curves and establish a predictive model based on the collected experimental data and calculated variance; and to optimize the next experiment based on the predictive model.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] This invention presents a split-plot experimental design analysis method that accurately determines the impact of various factors on the results of tasks constrained by both correlation and randomization by rapidly eliminating interfering factors. This improves the economy and adequacy (cost-effectiveness ratio) of experiments, enabling professional experimental personnel to develop more accurate experimental plans in a shorter time. Taking the success rate of UAV search missions as an example, the split-plot experimental design method quickly identifies key experimental factors, improving the success rate of UAV search missions. Simultaneously, it lays a solid foundation for supporting future mission-oriented simulation experiments of complex systems / architectures. Attached Figure Description

[0041] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] Example 1

[0046] like Figure 1 The diagram shown is a schematic representation of the method flow in this embodiment, and the steps include:

[0047] S1. Define the response variables and several experimental factors according to the experimental objectives, and determine the value level of each experimental factor.

[0048] Define the response variable, experimental factors, and value levels of each experimental factor in the experiment: First, the response variable needs to be determined according to the purpose of the experiment. The goal of this split-plot experiment is to explore the impact of different factors on the success rate of UAV search missions; the response variable for the split-plot experiment is the success rate of UAV search missions. Important experimental factors and their value levels are shown in Table 1.

[0049] Table 1

[0050] .

[0051] Subsequently, based on the actual situation and experimental objectives, appropriate experimental factors were selected for research, and the value levels of each experimental factor were determined.

[0052] The coding conversion formulas for each experimental factor within its corresponding sliding region are as follows:

[0053]

[0054] in, It is the encoded value of the sliding factor at point i when the main region factor A is at level j; This is the original value of the sliding factor at point i when the principal region factor A is at level j; is the original value of the center point of the sliding factor, Δ represents the radius of change of the sliding factor, and:

[0055]

[0056] in, and These represent the maximum and minimum values ​​of the sliding factor within the feasible experimental region when the main region factor A is at level j, respectively.

[0057] S2. Based on the value level of each experimental factor, construct the experimental design matrix according to the standard surface center design.

[0058] The constructed experimental design matrix is ​​a two-dimensional matrix, where each row represents an experimental point and each column represents a factor. The number of experimental points needs to be determined according to the design requirements. The constructed experimental design matrix completed in this embodiment is shown in Table 2:

[0059] Table 2

[0060] .

[0061] S3. Optimize the constructed experimental design matrix to obtain the optimized combination of experimental parameters.

[0062] The optimization of the experimental matrix must meet the following criteria: minimizing the frequency of changes in Hard To Change (HTC) factors during the experiment; repeating the experiment to ensure that the number of experiments in each sub-region is consistent; and arranging the linear and quadratic terms of the correlation factors in each region. The optimization results of the experimental matrix in this embodiment are shown in Table 3:

[0063] Table 3

[0064] .

[0065] S4. Arrange experiments according to the optimized combination of experimental parameters, collect experimental data and calculate variance.

[0066] S401. Based on the principal region and split region factors defined in the experimental design, the number of samples in the principal region is a, and the number of samples in the split region is b. The degrees of freedom are determined to be a-1 and b-1, respectively.

[0067] S402. Based on the degrees of freedom of each group of samples, calculate the sum of squares to further determine the estimated value of the variance corresponding to each source of variation.

[0068] If the main area error is The total variation in the main region is The cracking error is The total variation of the split zone is .

[0069]

[0070] Among them, SS T SS represents the total sum of squares, which is the sum of the squares of the differences between all observed values ​​and the total mean; M This represents the sum of squares of the principal regions, i.e., the sum of squares of the principal region processing combinations; SS B This represents the sum of squares of factors, specifically the sum of squares of factor B in the split zone; SS AB c represents the sum of squares of the A×B interaction; c represents the correction term. This represents the square of the sum of the blocks, that is, the sum of the squares of the sums of each block; The sum of the squares of the sums of the principal regions is calculated by summing the squares of the sums processed in each principal region; r represents the number of blocks; x 2 This represents the square of each observation.

[0071] S5. Based on the collected experimental data and calculated variance, fit the curve to establish a prediction model; and optimize the next experiment based on the prediction model.

[0072] Based on the experimental results, fit the curve and optimize the next experiment: Specifically, the experimental design requires fitting the following model:

[0073]

[0074] Where y represents the N×1 response vector; X represents the N×p fitted model matrix; β represents the p×1 fitted coefficient vector; σ represents the N×1 split-plot error vector; N represents the total number of trials; and p represents the terms included in the fitted model, including main effects, interaction effects, and secondary effects.

[0075] The expression for the covariance matrix E is as follows:

[0076]

[0077] in, This represents the squared error term of the cracked region; I represents the squared error term of the principal region; J represents the identity matrix; b J represents a block diagonal matrix. b The expression is as follows:

[0078] ,

[0079] Among them, I m J represents an m×m identity matrix; n Let represent an n×n matrix consisting entirely of 1s. Its matrix representation is as follows:

[0080] .

[0081] Since the covariance matrix is ​​no longer in the diagonal form of classical experimental design, applying OLS will severely reduce the accuracy of the results when the random disturbance term does not have homoscedasticity. Instead, GLS should be used for calculation. Generally, the estimated coefficients are calculated directly using OLS: Estimation with GLS They are different. For split-region designs, if there exists a... The non-singular matrix such that the design matrix satisfies At this point, the estimates of the coefficients calculated by OLS are equal to those calculated by GLS.

[0082] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method of split-plot trial based on dual restriction of association and randomization, characterized in that, The method comprises the following steps: S1, defining a response variable and several test factors according to a test purpose, and determining the value level of each test factor; S2, constructing a test design matrix according to the value level of each test factor according to a standard face center design; S3, optimizing the constructed test design matrix to obtain an optimized test parameter combination; S4, arranging a test according to the optimized test parameter combination, collecting test data and calculating variance; S5, fitting a curve to establish a prediction model based on the collected test data and calculated variance, and optimizing the next test based on the prediction model.

2. The method of the split-plot trial based on the dual restriction of association and randomization according to claim 1, wherein, The test factors include a main area factor and a sliding factor, wherein the main area factor is a difficult-to-change factor, and the sliding factor is an easy-to-change factor.

3. The method of claim 1, wherein, In S1, the encoding conversion formula of each test factor in the corresponding sliding area is: wherein, is the encoding value of the sliding factor at the i-th point when the main zone factor A takes the j-th level; is the original value of the sliding factor at the i-th point when the main zone factor A takes the j-th level, is the original value of the center point of the sliding factor when the main zone factor A takes the j-th level, and Δ represents the change radius of the sliding factor, and, wherein, and respectively represent the maximum and minimum values of the sliding factor within the feasible experimental region when the main zone factor A takes the jth level.

4. The method of claim 1, wherein, In S2, the method for constructing a test design matrix according to a standard face center design comprises: generating a two-dimensional matrix, wherein each row represents a test point, and each column represents a factor, and determining the number of test points according to design requirements.

5. The method of the split-plot trial based on the dual restriction of association and randomization according to claim 1, wherein, In S4, the step of calculating variance comprises: determining the variation sources in the variance analysis according to the main area and split area factors defined in the test design; calculating the degrees of freedom and sum of squares corresponding to each variation source according to the determined variation sources; calculating the estimated value of the variance component corresponding to each variation source based on the calculated degrees of freedom and sum of squares.

6. The method of the split-plot trial based on the dual restriction of association and randomization according to claim 1, wherein, In S5, the method for fitting a curve to establish a prediction model comprises: wherein y represents an N×1 response vector; X represents an N×p fitting model matrix; β represents a p×1 fitting coefficient vector; σ represents an N×1 split area error vector; N represents the total number of tests; and p represents the number of terms included in the fitting model.

7. The method of the split-plot trial based on the dual restriction of association and randomization according to claim 6, wherein, Parameter estimation using a covariance matrix improves the accuracy and reliability of the prediction model: The expression of the covariance matrix E is as follows: wherein represents the error square term of the split region; represents the error square term of the main region; I represents the unit matrix; J b represents the block diagonal matrix.

8. A split-plot system based on dual restriction by association and randomization for implementing the method of any one of claims 1 to 7, characterized in that, It comprises: a definition module, a design module, an optimization module, a calculation module, and a construction module; The definition module is used to define a response variable and several test factors according to a test purpose, and determine the value level of each test factor; The design module is used to construct a test design matrix according to the value level of each test factor according to a standard face center design; The optimization module is used to optimize the constructed test design matrix to obtain an optimized test parameter combination; The calculation module is used to arrange a test according to the optimized test parameter combination, collect test data and calculate variance; The construction module is used to fit a curve to establish a prediction model based on the collected test data and calculated variance, and optimize the next test based on the prediction model.

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