Inertial system performance evaluation method based on data reliability confidence rule base

Abstract

The application discloses an inertial system performance evaluation method based on a data reliability confidence rule base, which decomposes the inertial system evaluation problem into BRB-CDR modeling and evaluation real-time according to the characteristics of the inertial system itself, for the BRB-CDR modeling, the application adopts a statistical interval-based observation data reliability calculation method, constructs a BRB model considering data reliability, and analyzes the sensitivity of the BRB-CDR model output to the data reliability. In view of the real-time evaluation requirement, a time window size adaptive change strategy is designed, which takes into account the model training accuracy and training real-time. The experimental results show that the BRB-CDR model evaluation utility RMSE is reduced by 47.40% compared with the standard BRB model, by 52.27% compared with the BP neural network, and by 60.03% compared with the fuzzy reasoning system. Thus, the high precision and feasibility of the BRB-CDR model in the inertial system performance evaluation are verified.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation system technology, and more specifically to an inertial system performance evaluation method based on a data reliability confidence rule base. Background Technology

[0002] Inertial navigation systems (INS) act as sensors in aircraft positioning and navigation, and their performance greatly determines the accuracy of these systems. Due to fluctuations in manufacturing and assembly processes, as well as differences in the cumulative working time of individual systems, the performance of inertial instruments / systems varies considerably. Therefore, performance evaluation of inertial instruments / systems is crucial for selecting the best for critical missions, and is essential for improving navigation system performance and ensuring the successful execution of important tasks.

[0003] Current performance evaluation methods are mainly divided into three categories: expert knowledge-based evaluation methods, data-driven evaluation methods, and hybrid evaluation methods based on both expert knowledge and data-driven approaches. Expert knowledge-based evaluation methods (such as decision trees and fuzzy theory) involve analyzing the mechanistic mechanisms of inertial instruments based on expert knowledge and establishing evaluation models. The advantages of this method are a clear and transparent modeling process and strong traceability and interpretability of the model output. The disadvantage is that for complex systems, where the internal operating mechanisms are coupled and complex, limited and fuzzy expert knowledge makes it difficult to establish accurate evaluation models for complex systems. Data-driven evaluation methods (such as neural networks and support vector machines) rely entirely on sensor data, evaluating inertial instruments through data mining and learning. The advantage of this method is that it does not rely on any expert knowledge or prior knowledge. The disadvantage is that it requires a large amount of sample data, and the modeling process is not transparent. Hybrid evaluation methods based on both expert knowledge and data-driven approaches (such as confidence rule bases) evaluate inertial instruments simultaneously based on expert knowledge and sampled data. This method maximizes the use of available information, and the accuracy of performance evaluation depends on the quality of the hybrid data and expert knowledge approach. Reference [1] addresses the problem that existing research is highly sensitive to sample imbalance and proposes a model based on LSTM (Long-Term Short-Term Memory). This model combines SMART attributes and time analysis, and estimates the health status based on the failure time of the hard disk drive. Reference [2] addresses the performance evaluation problem of armored vehicle PHM system, establishes a performance measurement index system based on expert knowledge, determines the index weights using interactive hierarchical analysis, and uses fuzzy comprehensive analysis to determine the PHM system performance. Reference [3] addresses the bridge risk assessment problem, provides rule generation and reduction methods through parameter optimization and envelope, and obtains joint optimization of the extended confidence rule base. This method effectively reduces the complexity of the rule base and improves the evaluation accuracy.

[0004] However, inertial navigation systems (INS) are characterized by high reliability and high value, thus their performance evaluation exhibits the following four characteristics: First, high-precision INS used in aerospace (especially missile weapons) have extremely high reliability, limited cumulative service life, and high cost per instrument. Limited service life and high cost mean that numerous repeated experiments cannot be conducted; therefore, only a small number of high-value sample data can be obtained for high-precision INS instruments used in aerospace. Second, the internal operating mechanisms of INS are complex and coupled. Limited and fuzzy expert knowledge makes it difficult to analyze the mechanism of each component in the INS, meaning it is difficult to establish a high-precision evaluation model solely using expert knowledge. Third, INS are composed of various inertial instruments. Affected by the cumulative operating time of the instruments and random environmental factors, the sensitive data of the inertial instruments has a certain measurement error, meaning that the sensitive data has a certain degree of unreliability. This unreliability of sensitive data may reduce the accuracy of INS performance evaluation. Fourth, in the face of urgent missions (such as war), the time allotted for INS performance evaluation is extremely short, meaning that INS performance evaluation has high real-time requirements.

[0005] Based on the analysis of the characteristics of inertial navigation system performance evaluation problems, it can be seen that evaluation methods based on expert knowledge and data-driven methods are difficult to evaluate inertial system performance. Belief RuleBase (BRB), as a widely used performance evaluation method, integrates expert knowledge, evidence-based reasoning algorithms, etc. In the initial modeling stage of the Belief RuleBase, the model parameters are given based on the expert's cognitive knowledge of the system. Then, the model parameters are further trained based on observation data, thereby improving the accuracy of the evaluation model. This means that the Belief RuleBase can effectively integrate expert knowledge and observation data. However, the Belief RuleBase assumes that all raw data is completely reliable, without considering the reliability issues caused by instrument lifespan and random factors, which is inconsistent with engineering practice. Furthermore, inertial navigation system performance evaluation has high real-time requirements. Current methods to improve the real-time performance of Belief RuleBase evaluation involve reducing the structure of the Belief RuleBase, but this reduction in structure decreases the generalization ability of the Belief RuleBase. Summary of the Invention

[0006] To address the aforementioned problems, this invention considers the impact of data volume on the real-time performance evaluation, and that the latest data from historical observations best reflects the current performance state of the system. Therefore, by windowing and truncating historical observation data, the real-time evaluation is improved while maintaining the accuracy of the confidence rule base. In other words, this invention proposes a windowed confidence rule base evaluation method that considers data reliability for inertial system performance evaluation.

[0007] The core idea of ​​this invention is as follows: First, the performance evaluation problem of inertial systems is decomposed into several sub-problems, and three problems that the Belief Rule Base Considering Data Reliability (BRB-CDR) needs to solve are identified. Second, the data reliability calculation method is determined, and data reliability is integrated into rule activation and rule fusion to construct the BRB-CDR model, and the sensitivity of the model to data reliability is analyzed. Finally, in order to improve the real-time performance of model training and evaluation, an adaptive time window strategy is proposed, which makes the time window size adaptively change with the training error, thus balancing training accuracy and evaluation real-time performance.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A method for evaluating the performance of inertial systems based on a data reliability confidence rule base is characterized by the following steps:

[0010] Step 1: Construct the initial BRB-CDR model;

[0011] Step 2: Train the BRB-CDR model. First, establish a BRB-CDR parameter optimization model based on time windows; then, use the artificial bee colony algorithm to optimize the model parameters to obtain the optimized BRB-CDR model.

[0012] Step 3: Input the sample of the inertial system to be tested into the trained BRB-CDR model to obtain the performance evaluation results of the inertial system.

[0013] Furthermore, the specific steps of step 1 include:

[0014] Step 11: Define the data reliability of the BRB-CDR model and its calculation method;

[0015] Step 12: Calculate the feature matching degree of the BRB-CDR model;

[0016] Step 13: Calculate the regular activation weights of the BRB-CDR model;

[0017] Step 14: Fuse the activation rules of the BRB-CDR model.

[0018] Furthermore, the specific steps of step 11 include:

[0019] Step 111: Set the identifier parameter and define it as follows:

[0020]

[0021] Among them, y ijIndicates the identifier parameter; j represents the j-th observation data; x i (j) represents the j-th observation data of the i-th attribute; The mean of the characteristic observation data; σ is the adjustment coefficient; i Standard deviation;

[0022] Step 112: Set the statistical interval of feature i to According to equation (2), when x i (j) when y is within the statistical interval ij =1, otherwise y ij =0, the number of reliable data points y can be obtained. i for:

[0023]

[0024] Step 113: Define and calculate the reliability r of the i-th feature. i The formula is:

[0025]

[0026] And according to equations (2)-(4), we know that:

[0027] When r i =1 indicates that the data is completely reliable; r i =0 indicates that the data is completely unreliable.

[0028] Furthermore, the specific steps of step 12 include:

[0029] Step 121: For the i-th input feature x i (t), when x is ≤x i (t)≤x i(s+1) At that time, its matching degree with the k-th rule for:

[0030]

[0031] Where, x is This represents the reference value for the s-th level; The range of values ​​for is (0,1);

[0032] Step 122: Convert the different sensor information into a unified matching format according to equation (5).

[0033] Furthermore, the specific steps of step 13 include:

[0034] Step 131: Incorporate data reliability into the traditional BRB model to construct a new matching degree α of all features to the k-th rule. k(t) is:

[0035]

[0036] Where, δ i (t) represents the weight of feature i; r i (t) represents the reliability of the i-th feature;

[0037] Step 132: Define the rule activation weights for the k-th rule, considering all features related to data reliability, as follows:

[0038]

[0039] Where, ω k (t) represents the activation weight of the k-th rule; θ k (t) represents the weight of the k-th rule.

[0040] Furthermore, the specific steps of step 14 include:

[0041] Step 141: Set the confidence level β of the k-th rule's performance level. 1,k (t),β 2,k (t),…,β N,k (t) is transformed into the basic probability mass and the residual basic probability mass:

[0042] m n,k =ω k β n,k n = 1, 2, ..., N

[0043]

[0044]

[0045]

[0046] Where, m n,k Assigning the basic probability mass of rule k to performance level n; m D,k The remaining basic probability mass that is not assigned to any performance level; The remaining weight; For weighted residual probability quality;

[0047] Step 142: Denote the basic probability mass of the first k rules as m. n,br(k) The basic probability-quality fusion is performed by sequentially incorporating each rule, and the iterative formula for sequential rule incorporation is as follows:

[0048] m n,br(k) =K br(k) [m n,br(k-1) m n,k +mn,br(k-1) m D,k +m D,br(k-1) m n,k ]

[0049]

[0050]

[0051]

[0052]

[0053] Where, m n,br(k) The initial value is m n,1 ;m D,br(k) The initial value is m D,1 ; The remaining weights after fusing the first k-1 rules; The weighted residual probability quality is the fusion of the first k-1 rules;

[0054] Step 143: Based on the fused basic probability mass, obtain the confidence level of the system performance:

[0055]

[0056] Where, β n For the performance level D after rule fusion n The confidence level.

[0057] Step 144: Based on the rule fusion results, the performance evaluation results of the BRB-CDR model are as follows:

[0058] y = {(D1,β1),(D2,β2),…,(D N ,β N (12)

[0059] Where y represents the evaluation result; D N This refers to the system performance level.

[0060] Furthermore, the specific steps of step 2 include:

[0061] Step 21: Set a time window size range [T] min ,T max The time window size is defined to adapt to changing conditions as follows:

[0062]

[0063] Where T(t) is the time window scale at time t; e(t) is the training error at time t;

[0064] Step 22: Select N performance level confidence levels {β} n,k (t)}, n=1,2,…,N、M input feature weights {δ m (t)}, m=1,2,…,M、K rule weights {θ k (t)}, k=1,2,…,K are the parameters to be optimized;

[0065] Step 23: The objective function is to minimize the error between the assessed utility and the actual utility, and the root mean square error is used to measure the error between the assessed utility and the actual utility.

[0066]

[0067] Step 24: Define the constraints for the parameters to be optimized as follows:

[0068]

[0069] Step 25: Establish an optimization model for BRB-CDR parameters:

[0070] obj.min RMSE(β n,k (t),δ m (t),θ k (t))

[0071] steqs.(27) (28);

[0072] Step 26: Encode the parameters to be optimized as bee locations, set the nectar concentration to f = 1 / RMSE, and use the artificial bee colony algorithm to optimize formula (28) to obtain the optimized BRB-CDR model;

[0073] Step 27: Solve the optimized model from Step 26 to obtain the optimized model parameters, and then obtain the optimized BRB-CDR model.

[0074] Furthermore, based on the utility u(y) of the evaluation result y, a loss function is constructed for parameter optimization of the BRB-CDR model, and u(y) is:

[0075]

[0076] Compared with the prior art, the beneficial effects of this invention are:

[0077] This invention addresses the performance evaluation problem of inertial platform systems, integrating the advantages of expert knowledge and data-driven models, and establishing an evaluation model for inertial platform systems using a confidence rule base. To address the issue that confidence rule bases do not consider data reliability, a BRB-CDR model is proposed and constructed, and the sensitivity of the BRB-CDR model output to data reliability is analyzed. An adaptive strategy for the time window size based on training error is proposed, balancing training accuracy and real-time performance. Experimental results show that:

[0078] First, data reliability has a significant impact on the evaluation accuracy of the BRB model, and considering data reliability can effectively improve the evaluation accuracy of the BRB model.

[0079] Second, the BRB-CDR model constructed in this invention has significantly higher evaluation accuracy than the traditional BP network model and fuzzy inference system, proving that the BRB-CDR model achieves the integration of the advantages of expert knowledge and data-driven approaches. Attached Figure Description

[0080] Figure 1 This is a flowchart for calculating data reliability.

[0081] Figure 2 This is a screenshot of a time window.

[0082] Figure 3 This is a flowchart of the BRB-CDR evaluation process.

[0083] Figure 4 This is a performance index system for inertial platform systems.

[0084] Figure 5 This refers to changes in data reliability.

[0085] Figure 6 This shows the changes in the size of the time window.

[0086] Figure 7 This is a schematic diagram illustrating the training effect of the BRB-CDR model.

[0087] Figure 8 This is a sensitivity distribution chart for data reliability. Detailed Implementation

[0088] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0089] Based on the above core ideas, this invention proposes a performance evaluation method for inertial systems based on a data reliability confidence rule base. First, the performance evaluation problem of inertial systems is decomposed.

[0090] 1. Description and Modeling of Inertial System Performance Evaluation Problem

[0091] (1) Problem Description

[0092] Based on the above analysis, inertial navigation system performance evaluation exhibits four characteristics: small sample size, fuzzy expert knowledge, incomplete and unreliable data, and high real-time requirements. The existing BRB model first uses expert knowledge to establish an initial rule base, and then optimizes the rule base using observation data to address the low model accuracy caused by fuzzy expert knowledge. This indicates that while the existing BRB model can solve the problems of small sample size and fuzzy expert knowledge, it does not consider the issues of incomplete and unreliable data and high real-time requirements. Therefore, it can be determined that inertial navigation system performance evaluation includes the following sub-problems:

[0093] Question 1: Incorporating data reliability into the BRB model

[0094] Due to the influence of random and accidental environmental factors, inertial system sampling data inevitably contains measurement errors. This means that the sampling data of inertial systems is not completely reliable, and incompletely reliable observation data will inevitably reduce the accuracy of model evaluation. Existing BRB models treat data as completely reliable and do not consider the factors of data unreliability. Therefore, it is necessary to introduce data reliability into the BRB model to improve the evaluation accuracy of the BRB model.

[0095] Question 2: Real-time requirements for performance evaluation

[0096] In urgent missions such as war, the time available for evaluating the performance of inertial navigation systems (INS) is limited, meaning that INS evaluation requires high real-time performance. Therefore, it is necessary to address the issue of meeting the real-time performance evaluation requirements of INS.

[0097] (2) BRB Inertial System Evaluation Model Considering Data Reliability

[0098] To address the two issues mentioned above in the existing BRB model for inertial navigation system performance evaluation, a confidence rule base evaluation model that considers data reliability is proposed. Furthermore, a windowing method is used to extract data and optimize the evaluation model to improve the real-time performance evaluation.

[0099] In the BRB-CDR model, multiple confidence rules are set to reflect the nonlinear mapping relationship between input feature parameters and system performance states. The k-th rule considering data reliability is described as follows:

[0100]

[0101] Then y is{(D1,β 1,k (t)),(D2,β 2,k (t)),…,(D N,β N,k (t))}

[0102] With rule weightθ k (t),

[0103] characteristic weightδ1(t),δ2(t),…,δ M (t),

[0104] characteristic reliability r1(t),r2(t),…,r M (t),

[0105] and sliding time window T (1)

[0106] Among them, R k For the k-th rule; x1(t), x2(t), ... x M (t) represents M input features; M are the input feature reference values; y is the performance status evaluation result of the inertial navigation system; D1, D2, ... D N Let β represent the N performance levels of the system. 1,k (t),β 2,k (t),…,β N,k (t) represents the confidence level corresponding to the N performance levels; θ k (t) represents rule R k The weights; δ1(t), δ2(t), ..., δ M (t) represents the weights of the M input features; r1(t), r2(t), ..., r M (t) represents the reliability of the M input features; t represents the current time; T represents the time window used to improve the real-time performance evaluation.

[0107] Secondly, based on the above analysis, the BRB-CDR modeling problem is decomposed to obtain the key sub-problems to be solved; then, data reliability is defined and incorporated into the BRB model to obtain the BRB-CDR model; finally, the sensitivity of the BRB-CDR model to data reliability is derived.

[0108] 2. Performance evaluation model based on BRB-CDR

[0109] (1) Decomposition of BRB-CDR modeling problem

[0110] The main difference between the BRB-CDR model and the BRB model is that the BRB-CDR model considers data reliability, incorporating it into rule activation and fusion. Therefore, establishing a BRB-CDR model requires addressing the following three sub-problems:

[0111] Sub-problem 1.1: Definition and calculation of data reliability

[0112] Data reliability represents the ability of data to reflect the true state of the system. How to define and calculate data reliability, and how to accurately reflect the reliability of sampled data, has a great impact on the evaluation results of inertial systems.

[0113] Sub-problem 1.2: Integrating data reliability into the problem

[0114] The second issue that BRB-CDR needs to consider is how to incorporate data reliability into the BRB model so that it is reflected in the evaluation results.

[0115] Sub-problem 1.3: Sensitivity to data reliability

[0116] After incorporating data reliability into the BRB model, the sensitivity of the performance evaluation results (i.e., output) to data reliability should be quantitatively analyzed to determine whether the incorporation of data reliability is effective and to what extent.

[0117] (2) Data reliability calculation (solving sub-problem 1.1)

[0118] Data reliability represents the ability of sampled information to reflect the true state of the system. Common methods for calculating data reliability include distance-based methods and statistical interval-based methods. Statistical interval-based reliability calculation methods incorporate both objective statistical information from the sampled data and expert experience regarding parameter settings; therefore, this invention uses a statistical interval-based data reliability calculation method.

[0119] In practical engineering, the state of a system is relatively stable over a certain period of time. If the influence of random and accidental factors is not considered, the system output should remain stable within a small statistical range. However, due to the influence of random and accidental factors, the sensor output may exceed this statistical range, in which case the sampled data is considered unreliable. Based on this idea, a method is adopted as follows... Figure 1 The data reliability calculation process is shown below.

[0120] For the i-th feature observation data {x i (j)},j=1,2,…,q i The mean was calculated. and standard deviation σ i Then the statistical interval of feature i can be set as follows: in The adjustment coefficient is determined based on factors such as sensor sensitivity accuracy and expert experience. A larger value indicates a larger given statistical interval, meaning that experts have greater confidence in the collected data. A smaller value indicates a smaller given statistical interval, meaning that experts do not have enough trust in the collected data.

[0121] Set an identifier parameter y ij And defined as follows:

[0122]

[0123] y ij This represents the identifier parameter for the j-th observation of the i-th attribute, when x i (j) when y is within the statistical interval ij =1, y is not within the statistical interval ij =0, then the number of reliable data y can be obtained. i for:

[0124]

[0125] The reliability r of the i-th feature is calculated using equation (4). i for:

[0126]

[0127] By analyzing equations (2)-(4), it can be seen that when all observed data x i (j) When y is within the statistical interval i =q i At this time r i =1 indicates that the data is completely reliable; when all observed data x i When (j) are not within the statistical interval, y i =0, at this time r i =0 indicates that the data is completely unreliable.

[0128] (3) Construct the BRB-CDR model (solving sub-problem 1.3)

[0129] The construction process of the BRB-CDR model includes steps such as attribute matching, rule activation, rule fusion, and parameter optimization.

[0130] 1) Attribute matching

[0131] Sensor information from different sources and in different formats cannot be directly fused. For example, force signals measured by force sensors and temperature signals measured by temperature sensors have different dimensions and source domains, so they cannot be directly fused and need to be converted into a unified matching format.

[0132] For attribute i, the reference value for the s-th level is denoted as x. is Then for the i-th input attribute x at time t... i (t), when x is ≤x i (t)≤x i(s+1) At that time, its matching degree with the k-th rule for:

[0133]

[0134] Where L represents the number of rules.

[0135] Equation (5) can be used to convert sensor information from different sources and in different formats into a unified matching format, and The value range is (0,1), that is, different sensor information is converted into data between (0,1) by Equation (5).

[0136] 2) Rule activation

[0137] In the traditional BRB model, the matching degree α of all attributes to the k-th rule is... k (t) is:

[0138]

[0139] Where, δ i (t) represents the weight of attribute i.

[0140] The activation weights for rules that do not consider data reliability are:

[0141]

[0142] Where, ω k (t) represents the activation weight of the k-th rule.

[0143] As can be seen from equation (5), the matching degree If the value range is (0, 1), then combining equations (6) and (7), we can see that the weight δ of attribute i is... i The larger (t) is, the greater α becomes. k The smaller (t) is, the more ω k The smaller (t) is, the more unreasonable it is. To address this issue, we need to make the rule activation weight positively correlated with the attribute weight, while also incorporating data reliability. Therefore, we establish the matching degree α of all attributes to the k-th rule. k (t) is:

[0144]

[0145] Substituting equation (8) into equation (7), we can obtain the activation weight of rule k.

[0146] Analysis of equation (8) shows that the matching degree , and δ i (t)>0,r i (t)≥0, δ i (t)·r i (t)+1≥1, then , and α k (t)≥0. Additionally, when the weight δ i (t) and reliability r i As (t) increases, the matching degree α k (t) and activation weight ω k The increase in (t) is consistent with the real-world meaning, indicating that the matching degree α k The construction of (t) is reasonable.

[0147] 3) Rule integration

[0148] In a confidence rule base, multiple rules are activated, and each rule has a different evaluation result, thus requiring the fusion of activated rules. Evidential Reasoning (ER) algorithms are generally used for rule fusion. ER algorithms include analytical and recursive algorithms, with analytical ER algorithms having lower computational cost and recursive ER algorithms offering better traceability. To analyze the sensitivity of data reliability, this invention uses a recursive ER algorithm for rule fusion.

[0149] In the ER algorithm, the performance level confidence β of the k-th rule is... 1,k (t),β 2,k (t),…,β N,k (t) is transformed into the basic probability mass and the residual basic probability mass, as follows:

[0150] m n,k =ω k β n,k n = 1, 2, ..., N

[0151]

[0152]

[0153]

[0154] Where, m n,k Assigning the basic probability mass of rule k to performance level n; m D,k The remaining basic probability mass that is not assigned to any performance level; The remaining weight; This refers to the weighted residual probability quality.

[0155] In the recursive ER algorithm, the basic probability mass is fused by sequentially incorporating each rule, and the basic probability mass of the first k rules is denoted as m. n,br(k) The iterative formula for sequentially incorporating the rules is:

[0156] m n,br(k) =K br(k) [m n,br(k-1) m n,k +m n,br(k-1) m D,k +m D,br(k-1) m n,k ]

[0157]

[0158]

[0159]

[0160]

[0161] Where, m n,br(k) The initial value is m n,1 ;m D,br(k) The initial value is m D,1 .

[0162] Based on the fundamental probabilistic quality of the fusion, the confidence level of the system performance is obtained as follows:

[0163]

[0164] Where, β n For the performance level D after rule fusion n The confidence level.

[0165] Based on the rule fusion results, the output form of the BRB-CDR model, i.e., the inertial navigation system performance evaluation result y, is:

[0166] y = {(D1,β1),(D2,β2),…,(D N ,β N (12)

[0167] System performance level D n The utility is denoted as u(D) n If y is the result of the evaluation, then the utility of the evaluation result y is:

[0168]

[0169] Where u(y) represents the utility of the evaluation result.

[0170] Based on u(y), the loss function of the BRB-CDR model can be constructed during parameter optimization, thereby achieving model parameter optimization.

[0171] 4) Sensitivity Analysis

[0172] Because the sensitivity analysis method based on partial derivatives is highly operable and interpretable, this invention analyzes the sensitivity of the BRB-CDR model output to data reliability based on the partial derivative method. The derivation is first performed using a BRB-CDR model with two inputs and two rules as an example, and then extended to the general case.

[0173] First, the BRB-CDR model, which includes two inputs and two independent rules, is represented as follows:

[0174]

[0175] Based on equations (10) and (11), the basic probability mass and other parameters m of R1 and R2 can be calculated. n,br(1) m D,br(1) m n,br(2) m D,br(2) And performance level confidence levels β1 and β2.

[0176] Let B(r) be the sensitivity matrix of the BRB-CDR model output to data reliability r1 and r2. Then:

[0177]

[0178] Combining the expressions for β1 and β2 given in equation (11), the sensitivity matrix B(r) can be transformed into:

[0179] B(r)=N·W (16)

[0180] The matrices N and W are constructed as follows:

[0181]

[0182]

[0183] For matrix N, according to equation (11), we can obtain:

[0184]

[0185] For matrix W, let its element in the nth row and ith column be denoted as W(n,i). Combining with equation (10), we can obtain:

[0186] When n = 1, 2 and i = 1, 2, that is, for the elements in the first and second rows of matrix W, we have:

[0187]

[0188] When n = 3 and i = 1, 2, that is, for the elements in the 3rd row of matrix W, we have:

[0189]

[0190] Among them, in equations (19) and (20) The calculation formula is:

[0191]

[0192] In equations (19) and (20) The calculation formula is:

[0193]

[0194] Substituting equations (17) to (22) into equation (16), we can obtain the sensitivity matrix B(r) of the BRB-CDR model output to data reliability.

[0195] Secondly, the derivation process of the sensitivity matrix B(r) is generalized and extended. For a confidence rule base with M input attributes, N output levels, and L rules, its basic probability quality and performance level confidence can be calculated using equations (10) and (11). The confidence level β is then obtained. n For reliability r i The sensitivity is:

[0196]

[0197] The mean sensitivity of the BRB-CDR model output confidence level to reliability is then... for:

[0198]

[0199] Based on the sensitivity analysis results, parameters that are highly sensitive to data reliability can be identified, and targeted improvements can be made to the corresponding measurement conditions and hardware.

[0200] Finally, to mitigate the impact of limited, vague, and uncertain expert knowledge on the BRB-CDR model parameters, this invention trains the model parameters using sample data. Simultaneously, to improve training speed and real-time performance evaluation, an adaptive time window is used to extract sample data.

[0201] 3. Parameter optimization of BRB-CDR model based on time window

[0202] (1) Setting the time window size

[0203] To improve the real-time performance evaluation of the BRB-CDR model, this invention proposes an adaptive time window data extraction method.

[0204] In inertial system performance evaluation, observational data includes both current and historical sampled data. In BRB-CDR model training, generally, the larger the amount of data used in training, the higher the model's training accuracy, but the slower the training speed; conversely, the smaller the amount of data used in training, the lower the model's training accuracy, but the relatively faster the training speed. Furthermore, the performance state of an inertial system is dynamically changing, and the current state information contained in current and historical observations is inconsistent. Undoubtedly, the closer the observation data is to the current moment, the more accurately it reflects the system's current state.

[0205] Based on the above analysis, this invention uses an adaptive time window to extract observed data. When the training error is large, reducing the error is the primary objective, so a larger time window is used; when the training error is small, improving training speed is the primary objective, so a smaller time window is used. In this way, the time window size adaptively changes with the training error. The specific implementation method is as follows:

[0206] Set a time window size range [T] min ,T max The time window size adapts and changes as follows:

[0207]

[0208] In the formula: T(t) is the time window scale at time t; e(t) is the training error at time t. A schematic diagram of time window segmentation is shown below. Figure 2 As shown.

[0209] (2) BRB-CDR parameter optimization algorithm

[0210] To reduce the impact of the limitations and ambiguity of expert knowledge on the BRB-CDR model, the parameters of the BRB-CDR model are optimized based on data extracted using time windows.

[0211] In the BRB-CDR model, the parameters to be optimized include N performance level confidence levels {β}. n,k (t)}, n=1,2,…,N、M input attribute weights{δ m (t)}, m=1,2,…,M、K rule weights {θ k (t)}, k=1,2,…,K.

[0212] The optimization of BRB-CDR model parameters aims to minimize the error between the estimated utility and the actual utility of the model. The error between estimated and actual utility is measured using the root mean square error (RMSE), which is:

[0213]

[0214] In the formula: H is the amount of observed data within the time window; u(h) is the utility of the model evaluation; u re (h) represents the actual utility of the system.

[0215] During the optimization of BRB-CDR model parameters, the model parameters should comply with the following constraints:

[0216]

[0217] In summary, the optimized model for the BRB-CDR parameters is as follows:

[0218] obj.min RMSE(β n,k (t),δ m (t),θ k (t))

[0219] steqs.(27) (28)

[0220] For the parameter optimization model given in equation (28), based on the fact that the artificial bee colony algorithm has global optimization capabilities and the ability to escape local optima, this invention uses the artificial bee colony algorithm to optimize the parameter optimization model established in equation (28), setting the bee position code as the parameter to be optimized, i.e. (β n,k (t),δ m (t),θ k (t)), with the nectar source concentration set to f=1 / RMSE, and the optimized BRB-CDR model was obtained by optimizing the model parameters.

[0221] (3) Performance evaluation process of inertial system based on BRB-CDR

[0222] The performance evaluation process for inertial systems based on BRB-CDR is as follows: Figure 3 As shown, it mainly includes three steps: initial model building, model optimization, and performance evaluation.

[0223] Step 1: Initial Model Construction: Based on expert experience, set up the initial BRB-CDR model, including parameters such as rule weights, attribute weights, and level confidence.

[0224] Step 2: Model Optimization: Based on the training samples, the artificial bee colony algorithm is used to optimize the model parameters, reducing the impact of expert experience uncertainty on the model;

[0225] Step 3: Performance evaluation: Input the test sample into the optimized BRB-CDR model to obtain the evaluation results of the test sample.

[0226] Example

[0227] To further verify the feasibility and effectiveness of the method proposed in this invention, an inertial navigation system experiment was conducted to analyze the sensitivity of data reliability and compare the evaluation accuracy of various models.

[0228] 1. Experimental setup

[0229] This paper evaluates the inertial platform system of an aircraft, classifying it into four performance levels: Excellent (E), Good (G), Medium (M), and Poor (P). The performance level labels are based on navigation accuracy. Typically, an inertial platform system has six core measurement elements: three gyroscopes and three accelerometers. The measurement accuracy and reliability of accelerometers on the inertial platform are far greater than those of gyroscopes; therefore, the observation data from the three gyroscopes are selected to construct the attribute parameters. The relative error and zero-bias stability of the gyroscope output greatly reflect the gyroscope's measurement accuracy and stability; therefore, the zero-bias stability and relative error of the gyroscope observation data are used as attribute parameters. The experimental data are obtained from actual static test data of the inertial platform system after declassification.

[0230] Based on the gyroscope measurement data output by the inertial platform system, the zero-bias stability and relative measurement error information of the output data were extracted. A total of 480 sets of data were obtained under four performance levels. According to the principle of equality of each performance level, 400 sets of samples were selected as training samples, and the remaining 80 sets of samples were used as test samples.

[0231] Based on the preceding analysis, the performance index system for designing an inertial platform system, such as... Figure 4 As shown.

[0232] 2. Initial BRB-CDR model

[0233] In the inertial platform system, the X-axis, Y-axis, and Z-axis gyroscopes are identical, therefore the same reference level and reference value should be set. Four reference levels are selected for each gyroscope attribute: Large (B), Medium (M), Slightly Small (SL), and Small (L). Based on equipment data and expert experience, the reference levels and reference values ​​for gyroscope attributes are shown in Table 1.

[0234] Table 1. Attribute Reference Levels and Values

[0235]

[0236] according to Figure 4 The fluctuations in the gyroscope sampling data show that the data fluctuates irregularly, but the fluctuation range is relatively concentrated. This section will discuss the interval... As a statistical interval, it is used to calculate the reliability of the sampled data.

[0237] In the performance evaluation of a single gyroscope, two index attributes were selected for each gyroscope, and four reference levels were set for each attribute, resulting in 16 possible combinations. Therefore, there are 16 rules in the performance evaluation of a single gyroscope, and the gyroscope performance level is also divided into four levels: Excellent (E), Good (G), Average (M), and Poor (P). The initial BRB-CDR model was set by expert experience, as shown in Table 2.

[0238] Table 2 Initial BRB-CDR Model for Gyroscope Evaluation

[0239]

[0240]

[0241] The inertial platform system contains three gyroscopes along the X, Y, and Z axes. Each gyroscope has four performance levels, resulting in 64 possible rule arrangements. However, considering that the three gyroscopes in the inertial platform system are identical, there are only 20 possible rule combinations without considering the gyroscope arrangement order. The initial rule parameters were set by experts based on experience, as shown in Table 3.

[0242] Table 3 Initial BRB-CDR Model for System Evaluation

[0243]

[0244]

[0245] 3. Model Training

[0246] The BRB-CDR model parameters were trained using an artificial bee colony algorithm. The parameters to be optimized included 84 gyroscope-based BRB-CDR model parameters and 104 system evaluation-based BRB-CDR model parameters, totaling 188 model parameters. Therefore, the bee location encoding was a 188-dimensional parameter to be optimized, and the maximum number of optimization iterations was set to 200. Data reliability was determined based on data extracted within a time window using the statistical interval method. Since the training data extracted within the time window is dynamically changing, the resulting data reliability is also dynamically changing. Figure 5 As shown.

[0247] Depend on Figure 5It can be seen that the data reliability is mainly concentrated in the range of [80%, 100%], indicating that the data reliability is relatively high and can provide good data support for model training.

[0248] To improve the robustness of model training, the BRB-CDR model parameters were trained 20 times, and the best training result was used as the final parameters. To ensure model training accuracy, a sufficient amount of data should be used for training; therefore, the model size range was set to [1000, 600]. The time window size changes during model training as follows: Figure 6 As shown.

[0249] Depend on Figure 6 It can be seen that the time window size gradually decreases with the number of iterations in 20 training iterations, indicating that the model error gradually decreases during training. This is consistent with the actual training process and realizes the adaptive change of the time window size with the model error, balancing the training accuracy and real-time performance of the BRB-CDR model.

[0250] The optimal training result of the artificial bee colony algorithm was selected, with an RMSE of 0.1320. The comparison between the evaluated utility and actual utility of the model after optimal training is as follows: Figure 7 As shown.

[0251] Depend on Figure 7 It can be seen that the evaluation utility of the trained BRB-CDR model is in good agreement with the actual utility of the system, indicating that the BRB-CDR model has high evaluation accuracy for inertial system performance and can be used for performance evaluation of inertial platform systems.

[0252] After training, the optimized BRB-CDR model for gyroscope performance evaluation and the BRB-CDR model for acceleration measurement system performance evaluation are shown in Table 4 and Table 5, respectively.

[0253] Table 4. Optimized Gyroscope Evaluation BRB-CDR Model

[0254]

[0255]

[0256] Table 5 Optimized System Evaluation BRB-CDR Model

[0257]

[0258]

[0259] 4. Reliability Sensitivity Analysis

[0260] For the BRB-CDR performance evaluation model of the inertial platform system, the sensitivity of the BRB-CDR model to data reliability is analyzed. Based on the sensitivity calculation method described above, the mean sensitivity of the model output to data reliability is obtained, and the results are as follows: Figure 8 As shown.

[0261] Depend on Figure 8 It can be seen that the model output's sensitivity to the reliability of the X-axis, Y-axis, and Z-axis gyroscope data is not significantly different. This is because in the platform stabilization system, each of the three gyroscopes is responsible for stabilization in one direction, and the platform's stability in all three directions is crucial. Therefore, the model output's sensitivity to the reliability of the X-axis, Y-axis, and Z-axis gyroscope data is not significantly different. However, a closer comparison reveals that overall, the model output is most sensitive to the reliability of the X-axis gyroscope, followed by the Z-axis, with the Y-axis being the least sensitive. This is because the X-axis gyroscope points in the direction of impact within the firing plane, and its measurement reliability greatly affects the missile's longitudinal error, hence its highest sensitivity. The Z-axis gyroscope is perpendicular to the firing plane, and its measurement reliability greatly affects the missile's lateral error, thus the model output is also most sensitive to the Z-axis gyroscope's reliability. The Y-axis gyroscope points upwards within the firing plane, and its measurement reliability indirectly affects the lateral error, but since the aircraft's flight altitude can generally be effectively adjusted and controlled, the system output's sensitivity to the Y-axis gyroscope's reliability is relatively the lowest.

[0262] From an engineering application perspective, the sensitivity analysis results of data reliability can provide guidance for platform system design. The sensitivity analysis results indicate that all three gyroscopes should receive sufficient attention in terms of financial, technological, and human resource investment, but a slight bias towards the X-axis and Z-axis gyroscopes is acceptable. Furthermore, regarding gyroscope installation, the gyroscope with the best performance should be installed along the X-axis, followed by the Z-axis, and then the Y-axis.

[0263] 5. Model accuracy testing and comparison

[0264] To verify the accuracy of BRB-CDR performance evaluation, this invention designs three comparison methods.

[0265] First, an inertial system evaluation model was established using the standard BRB model and compared with the BRB-CDR model to verify the role of data reliability in improving model accuracy.

[0266] Second, we used a backpropagation (BP) neural network, a completely data-driven model, and compared it with the BRB-CDR model to verify the role of expert experience in improving model accuracy.

[0267] Third, the initial BRB model was transformed into a fuzzy inference system. The fuzzy inference system is a complete expert system without the participation of sample data. It was compared with the BRB-CDR model to verify the role of sample data-driven improvement in model accuracy.

[0268] In the above methods, the BRB-CDR model and the standard BRB model are optimized using the artificial bee colony algorithm, while the BP neural network parameters are optimized using the traditional gradient descent method. The test samples are input into the above evaluation model, and the RMSE of the actual utility and the evaluated utility are shown in Table 6.

[0269] Table 6 Evaluation accuracy of different models

[0270]

[0271] As shown in Table 6, the RMSE of the BRB-CDR model is 0.1548, which is 47.40% lower than the standard BRB model, 52.27% lower than the BP neural network, and 60.03% lower than the fuzzy inference system.

[0272] Experimental results show that:

[0273] (1) Considering that data reliability can effectively improve the evaluation accuracy of the model, it shows that data reliability has a significant impact on the evaluation accuracy of the model.

[0274] (2) The evaluation accuracy of the model driven by a mixture of expert knowledge and data (BRB-CDR model) is higher than that of the pure data-driven model (BP network) and the pure expert knowledge model (fuzzy reasoning system), indicating that the BRB-CDR model has achieved the integration of the advantages of expert knowledge and data-driven approaches.

[0275] References:

[0276] Document [1] "De Santo A, Galli A, Gravina M, et al. Deep Learning for HDD health assessment: An application based on LSTM [J]. IEEE Transactions on Computers, 2020, 71(1): 69-80."

[0277] Reference [2] “Wang Guanqiu, Zheng Guojie, Feng Fuzhou, et al. Performance evaluation of armored vehicle PHM system based on fuzzy hierarchical analysis [J]. Computer Measurement & Control, 2021, 29(06):239-244.”

[0278] Reference [3] “Yang Longhao, Ye Feifei, Wang Yingming. Bridge risk assessment based on joint optimization of extended confidence rule base [J]. Systems Engineering Theory & Practice, 2020, 40(07): 1870-1881.”

[0279] The foregoing has shown and described the basic principles, main attributes, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for evaluating the performance of inertial systems based on a data reliability confidence rule base, characterized in that, Includes the following steps: Step 1: Construct the initial BRB-CDR model; the BRB-CDR model is a confidence rule base that considers data reliability; Step 2: Train the BRB-CDR model. First, establish a BRB-CDR parameter optimization model based on time windows; then, use the artificial bee colony algorithm to optimize the model parameters to obtain the optimized BRB-CDR model. Step 3: Input the sample of the inertial system to be tested into the trained BRB-CDR model to obtain the performance evaluation results of the inertial system; The specific steps of step 1 include: Step 11: Define the data reliability of the BRB-CDR model and its calculation method; Step 12: Calculate the feature matching degree of the BRB-CDR model; Step 13: Calculate the regular activation weights of the BRB-CDR model; Step 14: Fuse the activation rules of the BRB-CDR model; Step 13 includes the following specific steps: Step 131: Incorporate data reliability into the traditional BRB model to construct a new set of all feature pairs. Matching degree of the rule for: （8） in, Representation of features The weights; This represents the reliability of the i-th feature; Step 132: Define all features that consider data reliability for the first... The rule activation weight of this rule is: ； in, For the first The activation weight of each rule; Let be the weight of the k-th rule.

2. The inertial system performance evaluation method based on a data reliability confidence rule base as described in claim 1, characterized in that, Step 11 includes the following specific steps: Step 111: Set the identifier parameter and define it as follows: （2） in, This indicates the identifier parameter; j represents the j-th observation data; For the first The j-th observation data of each attribute; The mean of the characteristic observation data; This is the adjustment coefficient; Standard deviation; Step 112: Add features The statistical interval is set to According to equation (2), when When within the statistical interval ,otherwise A large amount of reliable data can be obtained. for: （3）； Step 113: Define the calculation of the first... Reliability of each feature The formula is: （4）； And according to equations (2)-(4), we know that: when This indicates that the data is completely reliable; This indicates that the data is completely unreliable.

3. The inertial system performance evaluation method based on a data reliability confidence rule base as described in claim 2, characterized in that, Step 12 includes the following specific steps: Step 121: For the i-th input feature ,when At that time, it was for the first Matching degree of the rule for: （5） in, Indicates the first Reference values ​​for each level; The range of values ​​for is (0,1); Step 122: Convert the different sensor information into a unified matching format according to equation (5).

4. The inertial system performance evaluation method based on a data reliability confidence rule base as described in claim 1, characterized in that, Step 14 includes the following specific steps: Step 141: Place the first Rule performance level confidence Transformed into basic probability mass and residual basic probability mass: （9） in, For rules Assigned to performance level The basic probability mass; The remaining basic probability mass that is not assigned to any performance level; The remaining weight; For weighted residual probability quality; Step 142: Place the front The basic probability mass of the rule is denoted as The basic probability-quality fusion is performed by sequentially incorporating each rule, and the iterative formula for sequential rule incorporation is as follows: （10） in, The initial value is ; The initial value is ; The remaining weights after fusing the first k-1 rules; The weighted residual probability quality is the fusion of the first k-1 rules; Step 143: Based on the fused basic probability mass, obtain the confidence level of the system performance: （11） in, For the performance level after rule fusion Confidence level; Step 144: Based on the rule fusion results, the performance evaluation results of the BRB-CDR model are as follows: （12） Where y represents the evaluation result; D N This refers to the system performance level.

5. The inertial system performance evaluation method based on a data reliability confidence rule base as described in claim 1, characterized in that, Step 2 includes the following specific steps: Step 21: Set a time window size range Define the time window size to adapt as follows: （25） in, for The time window scale of a given moment; for Training error at any given time; Step 22: Select Confidence level of each performance level , Input feature weights , Each rule weight These are the parameters to be optimized. Step 23: The objective function is to minimize the error between the assessed utility and the actual utility, and the root mean square error is used to measure the error between the assessed utility and the actual utility. （26） In the formula: The amount of observation data within the time window; The utility of the model is evaluated; For the actual utility of the system; Step 24: Define the constraints for the parameters to be optimized as follows: （27）； Step 25: Establish an optimization model for BRB-CDR parameters: （28）； Step 26: Encode the parameter to be optimized as bee location, and set the nectar concentration to... The optimized BRB-CDR model was obtained by using the artificial bee colony algorithm to optimize formula (28); Step 27: Solve the optimized model from Step 26 to obtain the optimized model parameters, and then obtain the optimized BRB-CDR model.

6. The inertial system performance evaluation method based on a data reliability confidence rule base as described in claim 4, characterized in that, Based on the utility of the evaluation result y The loss function for parameter optimization when constructing a BRB-CDR model, and for: （13） in, For performance level Its effectiveness.

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