LU505180B1 - Optimization method of network-electric efficiency evaluation model based on numerical inverse problem - Google Patents
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Abstract
The invention discloses an optimization method of network-electric efficiency evaluation model based on numerical inverse problem, and the method includes following steps: extracting indexes related to the network-electric efficiency, establishing an index system for evaluating the efficiency, and setting the weight of each index; establishing a fuzzy mapping from the evaluation index system to the network-electric efficiency, and using the S-type function to modify the index weight, and substituting the index value and the modified weight into the fuzzy mapping function to obtain a quantitative evaluation model of the network-electric efficiency; under the condition that the index value is known, establishing an inverse problem model for optimizing the index weight by evaluating the power efficiency of the network in the model through a least square method; applying a regularization to the inverse problem model to suppress the numerical ill-condition, that is, adding a regularization penalty function term to the inverse problem mathematical model; using Newton-Raphson iterative algorithm to solve the regularized inverse problem model to obtain the optimal weight. The invention optimizes the network-electric efficiency evaluation model through the existing simulation and experimental data, and improves the accuracy of the evaluation result.
Description
OPTIMIZATION METHOD OF NETWORK-ELECTRIC
EFFICIENCY EVALUATION MODEL BASED ON NUMERICAL
INVERSE PROBLEM
The invention belongs to the technical field of military communication network efficiency evaluation, and in particular to an optimization method of network-electric efficiency evaluation model based on numerical inverse problem.
As the fifth battlefield of the future war, network electromagnetic space is highly dynamic and has strong security measures, which makes it very difficult to describe its operational effectiveness and the related research results are also scarce. In military activities, how to accurately evaluate the operational effectiveness of a battlefield communication network is the key to formulate strategies and tactics, reasonably and efficiently command network-electric attacks, and is also of great significance to the theoretical development of communication countermeasures.
The evaluation of network-electric efficiency involves multi-dimensional indicators, which often have different dimensions and intersect with each other, so it is necessary to extract a reasonable and complete index system to establish a network-electric efficiency evaluation model. At present, some related researches have put forward network-electric efficiency evaluation models based on Metcalfe's law, ADC efficiency function and topology destruction, but the accuracy of the model is low and there is no effective mathematical algorithm to optimize the model. There is little research on the optimization method of network-electric efficiency evaluation model, which leads to the low accuracy of the established evaluation model in practical application and is difficult to provide effective guidance for military command in the battlefield.
SUMMARY LU505180
The purpose of the invention is to provide an optimization method of network-electric efficiency evaluation model based on numerical inverse problem, so as to improve the accuracy and universality of the evaluation model, and thus providing theoretical basis for command and control in network power actual combats.
The technical solution for realizing the purpose of the invention is as follows: the optimization method of the network-electric efficiency evaluation model based on the numerical inverse problem includes following steps: step 1, extracting indexes related to the network-electric efficiency, establishing an index system for evaluating the efficiency, and setting the weight of each index; step 2, establishing a fuzzy mapping from the evaluation index system to the network-electric efficiency, and using the S-type function to modify the index weight, and substituting the index value and the modified weight into the fuzzy mapping function to obtain a quantitative evaluation model of the network-electric efficiency; step 3, under the condition that the index value is known, establishing an inverse problem model for optimizing the index weight by evaluating the power efficiency of the network in the model through a least square method; step 4, applying a regularization to the inverse problem model to suppress the numerical ill-condition, that is, adding a regularization penalty function term to the inverse problem mathematical model; step 5, using Newton-Raphson iterative algorithm to solve the regularized inverse problem model to obtain the optimal weight.
Further, in the step 1, extracting indexes related to the network-electric efficiency, establishing an index system for evaluating the efficiency, and setting the weight of each index, specifically as follows: extracting the indicators related to network-electric efficiency, including frequency band utilization rate, channel utilization rate, network capacity, transmission delay, bit error rate, packet loss rate, signal-to-noise ratio, network connectivity, mobility and survivability, establishing an index system k=(k,k,,,k,) for evaluating efficiency, k,k,,---,k, indicate the first to N indicators in sequence, and setting the weights of each index as w, =(w,,w, ,---,w, ) through expert evaluation, and ww, ,---,w, are the weights of the indicators k,k,,,k,.
Further, in the step 2, establishing a fuzzy mapping from the evaluation index system to the network-electric efficiency, and using the S-type function to modify the index weight, and substituting the index value and the modified weight into the fuzzy mapping function to obtain a quantitative evaluation model of the network-electric efficiency, specifically as follows: establishing the fuzzy mapping FE=f(k) of the evaluation index system to the network-electric efficiency, and modifying the index weight by S-function, and obtaining the quantitative evaluation model of the network-electric efficiency
X 1
BY rk by substituting the index value and weight into the fuzzy mapping io 1+e * function, where f(0) represents the mapping function relationship between the index value and the network efficiency, Æ represents the network-electric efficiency, K; represents the i-th index quantization value, and w; represents the i-th index weight.
Further, in the step 3, under the condition that the index value is known, establishing an inverse problem model for optimizing the index weight by evaluating the power efficiency of the network in the model through a least square method, specifically as follows: under the condition that the index is known, the network-electric efficiency 1s
Nk
E=f 00) Een and the inverse problem model for optimizing the index io te * weight is as follows: . 2 N 2 min e(w,) = | fw) El => (f6w,)- E,) i=l
Wy = (We Wy ew)
S00) =o foros)
E=(E.E,,- E,) where e(w,) represents the difference between the calculated efficiency value and the actual accurate efficiency expressed by the least square method; wz represents the index weight vector, and the component w, of wy is the corresponding weight of each index; f(w,) represents the network-electric efficiency calculated by known indicators and weights, and the component f,(w,) of f(w,) isthe efficiency value calculated by each group of indicators; E represents the accurate power efficiency value obtained by simulation or experiment, and the component £ of E is the accurate efficiency value corresponding to each group of indicators; N represents the number of indicators, and m represents the number of simulations or experiments, that is, the number of groups with known indicator values.
Further, in the step 4, applying a regularization to the inverse problem model to suppress the numerical ill-condition, that is, adding a regularization penalty function term to the inverse problem mathematical model, specifically as follows: applying the regularization to the inverse problem model to suppress the numerical ill-condition, that is, _ 2 ©) _ yp ON min e(wy) =| fw) —E| tor Low, —w, ) where œ represents a regularization parameter, L represents regularization matrix, s represents iteration times, w,” represents initial index weight and w,“ represents index weight of the s-th iteration.
Further, in the step 5, using Newton-Raphson iterative algorithm to solve the regularized inverse problem model to obtain the optimal weight, specifically as follows: the iteration format is as follows:
A, = III, +aLL) If) E)+ aL" Low,” =w,)]
Mm = 1,0 + Aw, where J represents the Jacobian matrix of network-electric efficiency to index weight, f(w,) and Aw, respectively represent the corresponding calculation efficiency value and index weight iteration difference when the iteration number is s, 5 w,”" isthe index weight value obtained after s-step iteration.
Compared with the prior art, the method has the following obvious advantages: (1) an optimization model and a solving algorithm of the network-electric efficiency evaluation model are established, and the accuracy and universality of the evaluation model can be effectively improved through solving; (2) the whole model optimization process is based on numerical algorithm, which has high efficiency and accuracy. The regularization method reduces the numerical ill-condition of the inverse problem optimization model, improves the stability and accuracy of the algorithm, and the
Newton-Raphson iterative algorithm improves the convergence speed of the model solution.
FIG. 1 is a flow chart of the optimization method of the network-electric efficiency evaluation model based on the numerical inverse problem of the present invention.
FIG. 2 is a schematic diagram of the convergence process of the difference between the calculated efficiency value and the accurate efficiency value of the model in the iterative process.
FIG. 3 is a correction graph of the S-shaped curve to the weight interval (-5,5).
Aiming at the optimization problem of the efficiency evaluation model of the network-electric efficiency communication system in the network-electric combined HUS05T80 attack, the invention provides an optimization method of network-electric efficiency evaluation model based on numerical inverse problem. By establishing the inverse problem model of the network-electric efficiency to the index weight, the weight is optimized through simulation and experimental data, and the optimal weight vector is obtained by iterative solution, so as to improve the accuracy and universality of the evaluation model. Therefore, it is of great significance to provide theoretical basis for the command and control in actual combat.
With reference to FIG. 1, an optimization method of network-electric efficiency evaluation model based on numerical inverse problem of the present invention includes following steps: the optimization method of the network-electric efficiency evaluation model based on the numerical inverse problem includes the following steps: step 1, extracting indexes related to the network-electric efficiency, establishing an index system for evaluating the efficiency, and setting the weight of each index; step 2, establishing a fuzzy mapping from the evaluation index system to the network-electric efficiency, and using the S-type function to modify the index weight, and substituting the index value and the modified weight into the fuzzy mapping function to obtain a quantitative evaluation model of the network-electric efficiency; step 3, under the condition that the index value is known, establishing an inverse problem model for optimizing the index weight by evaluating the power efficiency of the network in the model through a least square method; step 4, applying a regularization to the inverse problem model to suppress the numerical ill-condition, that is, adding a regularization penalty function term to the inverse problem mathematical model; step 5, using Newton-Raphson iterative algorithm to solve the regularized inverse problem model to obtain the optimal weight.
Further, in the step 1, extracting indexes related to the network-electric efficiency, establishing an index system for evaluating the efficiency, and setting the weight of each index, specifically as follows:
extracting the indicators related to network-electric efficiency, including HUS05T80 frequency band utilization rate, channel utilization rate, network capacity, transmission delay, bit error rate, packet loss rate, signal-to-noise ratio, network connectivity, mobility and survivability, establishing an index system
K=(k,k,,k,) for evaluating efficiency, k,k,,---,k, indicate the first to N indicators in sequence, and setting the weights of each index as w, =(w,,w, ,---,w, ) through expert evaluation, and ww, ,---,w, are the weights of the indicators k,k,,,k,.
Further, in the step 2, establishing a fuzzy mapping from the evaluation index system to the network-electric efficiency, and using the S-type function to modify the index weight, and substituting the index value and the modified weight into the fuzzy mapping function to obtain a quantitative evaluation model of the network-electric efficiency, specifically as follows: establishing the fuzzy mapping FE=f(k) of the evaluation index system to the network-electric efficiency, and modifying the index weight by S-function, and obtaining the quantitative evaluation model of the network-electric efficiency
X 1
B=) ok by substituting the index value and weight into the fuzzy mapping function, where f(0) represents the mapping function relationship between the index value and the network efficiency, Æ represents the network-electric efficiency, 4; represents the i-th index quantization value, and w; represents the i-th index weight.
Further, in the step 3, under the condition that the index value is known, establishing an inverse problem model for optimizing the index weight by evaluating the power efficiency of the network in the model through a least square method, specifically as follows: under the condition that the index is known, the network-electric efficiency is
Nk
E=f ENT and the inverse problem model for optimizing the index weight is as follows: 2 N 2 min e(w,) = If Ow) —E| => (fw) —F)) i=l
Wy = (We Wy ew)
S00) =o foros)
E=(E.E,,- E,) where e(w,) represents the difference between the calculated efficiency value 5 and the actual accurate efficiency expressed by the least square method; wi represents the index weight vector, and the component w, of wy is the corresponding weight of each index; f(w,) represents the network-electric efficiency calculated by known indicators and weights, and the component f(w,) of f(w,) isthe efficiency value calculated by each group of indicators; E represents the accurate power efficiency value obtained by simulation or experiment, and the component £ of E is the accurate efficiency value corresponding to each group of indicators; N represents the number of indicators, and m represents the number of simulations or experiments, that is, the number of groups with known indicator values.
Further, in the step 4, applying a regularization to the inverse problem model to suppress the numerical ill-condition, that is, adding a regularization penalty function term to the inverse problem mathematical model, specifically as follows: applying the regularization to the inverse problem model to suppress the numerical ill-condition, that is, _ 2 ©) _ yp ON min e(wy) =| fw) —E| tor Low, —w, ) where œ represents a regularization parameter, L represents regularization matrix, s represents iteration times, w,” represents initial index weight and w,“ represents index weight of the s-th iteration.
Further, in the step 5, using Newton-Raphson iterative algorithm to solve the regularized inverse problem model to obtain the optimal weight, specifically as follows:
1, LU505180 the iteration format is as follows: —1
Aw © =<(J1J,+a[L) [J] (fw) = E)+al Low, ww.) (s+) _ (s) (s)
WE = ww + Aw, where J represents the Jacobian matrix of network-electric efficiency to index weight, f(w,) and Aw, respectively represent the corresponding calculation efficiency value and index weight iteration difference when the iteration number is s, w, “is the index weight value obtained after s-step iteration.
Next, the invention is further described in detail with the attached drawings and the specific embodiment.
The embodiment provides an optimization method of network-electric efficiency evaluation model based on numerical inverse problem, which includes following steps: (1) establishing an index system having a close impact on the power efficiency of the network, and obtaining Kk=(k,k,,k,) by numerical quantification and dimensionless processing on indexes, setting the initial value wi = (www) of the weight vector of the index system, and establishing y 1 a calculation model E= f(k)= > — for evaluating the network-electric i +e "* efficiency. (2) through the simulation or historical experimental data, establishing an accurate data set of m groups of index system values to the network-electric efficiency
E, that is k=( ky, ky) > Ey ky =(kyy bye ky) > I, k, =k, kp Kim) >b a . . . . . LU505180 (3) substituting the index values in (2) above into the efficiency evaluation calculation model in (1), and calculating m groups of efficiency values, which will be different from the simulation or experimental data values in (2), so it is necessary to improve and optimize the weights. When a set of weight vectors is sought to minimize the difference between the calculated value and the actual value of the efficiency evaluation model, the evaluation model is optimal at this time, so establishing the inverse problem optimization model as follows: ; 2 X 2 min e(w,) = If Ow) —E| => (fw) —F)) i=l (4) The inverse problem is ill-conditioned in numerical solution. In order to suppress the ill-conditioned, the model in (3) is applied with a regularization, that is _ 2 ©) _ yp ON min e(wy) =| fw) —E| tor Low, —w, ) wherein & represents a regularization parameter, L represents regularization matrix, s represents iteration times, w,” represents initial index weight. (5) using the Newton-Raphson iterative algorithm to solve the inverse problem model with regularization in (4), and the iterative formula is as follows. -1
Mw = (JI +al'L) [J] (fw) = E)+al Low, ww.) wD =p Oy A ©) where J, represents the Jacobian matrix of network-electric efficiency to index weight, that is
HO 9d ow, ow ow, 9h oh Yh
J= ow, ow, ow,
Gn Un. Yn ow, ow, ow, the result of iterative solution is the optimized index weight vector, and then it is substituted into the efficiency evaluation model in (1) to obtain the optimized network-electric efficiency evaluation model.
A numerical model of quantitative inverse problem for calculating the weight of HUS05T80 optimization index with known network-electric efficiency is established, and the model is solved by regularization and Newton-Raphson iteration method. The weight is corrected by using S-function, and the linear influence of index weight on network-electric efficiency is nonlinear.
Combined with the attached drawings and the embodiment, the specific implementation method is as follows: it is assumed that the established network-electric efficiency index system contains 10 indexes (i.e. N=10), and the initial weight vector of the index is: w,®=(0.7720,0.9329,0.9727,0.1920,0.1389,0.6963,0.0938,0.5254,0.5303,0.8611)" groups of data (i.e. m=10) are collected through simulation or experiment, and the index system values and corresponding efficiency values are as follows:
Class k value of index system Network-elec numb tric efficiency er E 1 0.4849, 3.6846 0.7363,0.3968,0.5144,0.4952,0.6126,0.6260,0.5523,0.5386,0 .9479 2 0.3935,0.3947,0.8085,0.8843,0.1897,0.9900,0.6609,0.6299,0 3.5448 .6952,0.0821 3 0.6714,0.6834,0.7551,0.5880,0.4950,0.5277,0.7298,0.0320,0 3.2617 4991,0.1057 4 0.7413,0.7040,0.3774,0.1548,0.1476,0.4795,0.8908,0.6147,0 3.2379 .5358,0.1420 5 0.5201,0.4423,0.2160,0.1999,0.0550,0.8013,0.9823,0.3624,0 2.6101 4452,0.1665 6 0.3477,0.0196,0.7904,0.4070,0.8507,0.2278,0.7690,0.0495,0 2.5079 .1239,0.6210 7 0.1500,0.3309,0.9493,0.7487,0.5606,0.4981,0.5814,0.4896,0 3.7890
.4904,0.5737 HUS05180 8 0.5861,0.4243,0.3276,0.8256,0.9296,0.9009,0.9283,0.1925,0 3.8344 .8530,0.0521 9 0.2621,0.2703,0.6713,0.7900,0.6967,0.5747,0.5801,0.1231,0 4.1023 .8739,0.9312 10 0.0445,0.1971,0.4386,0.3185,0.5828,0.8452,0.0170,0.2055,0 2.4669 .2703,0.7287 11 0.7549,0.8217,0.8335,0.5341,0.8154,0.7386,0.1209,0.1465,0 3.9639 .2085,0.7378 12 0.2428,0.4299,0.7689,0.0900,0.8790,0.5860,0.8627,0.1891,0 2.8422 .5650,0.0634 13 0.4424,0.8878,0.1673,0.1117,0.9889,0.2467,0.4843,0.0427,0 3.0347 .6403,0.8604 14 0.6878,0.3912,0.8620,0.1363,0.0005,0.6664,0.8449,0.6352,0 3.6237 4170,0.9344 15 0.3592,0.7691,0.9899,0.6787,0.8654,0.0835,0.2094,0.2819,0 3.8321 .2060,0.9844
Substituting the index system values and initial weights in the above table into 10 1 the efficiency function relationship Sf (w,©) = 2k, and calculating the i=l [+e *
Jacobian matrix J,.
Setting the regularization parameter a = 0.0005, and the regularization matrix L is 10x10 unit matrix.
Substituting the above data into Newton-Raphson iteration formula to obtain the first iteration result, then repeating the efficiency value and Jacobian matrix of the previous step, and substituting the iterative formula for the calculation until the difference between the calculated efficiency value and the accurate value is the minimum, that is, the iteration is over.
The difference between the calculated efficiency value of the model and the accurate efficiency value in the iterative process is shown in FIG. 2, and the optimal HUS05T80 weight set obtained from the iterative results is w=(1.4898,0.4482,1.7832,1.1514,0.1057,-0.0762,-1.0761,0.6956,3.0176,1.0009)
T > combined with FIG. 3, the corrected weights obtained by S-shaped curve correction are as follows
Ww =(0.8160,0.6102,0.8561,0.7598,0.5264,0.4810,0.2542,0.6672,0.9534,0.7312)" Then the efficiency evaluation model of network-electric efficiency under this index system is as follows: £ = 0.8160k, + 0.6102k, +0.8561k, + 0.7598k, + 0.5264k, + 0.4810k, + 0.2542k, + 0.6672k, + 0.9534k, +0.7312kp
To sum up, the invention establishes a fuzzy mapping model from the grid power efficiency evaluation index system to the grid power efficiency, and nonlinearizes the index weight through the S-shaped curve. In order to improve the accuracy of the model, a numerical model of the inverse problem is established, and a regularization algorithm 1s applied to the mathematical model of the inverse problem to suppress the ill-condition of the inverse problem, and the model is solved by Newton-Raphson iterative algorithm. The numerical optimization model of inverse problem can optimize the index weight in the evaluation model by using the known simulation or experimental data, and obtain the most reasonable and universal weight vector, thus effectively improving the accuracy of the evaluation model.
Claims (6)
1. An optimization method of network-electric efficiency evaluation model based on the numerical inverse problem, characterized by comprising following steps: step 1, extracting indexes related to the network-electric efficiency, establishing an index system for evaluating the efficiency, and setting the weight of each index; step 2, establishing a fuzzy mapping from the evaluation index system to the network-electric efficiency, and using the S-type function to modify the index weight, and substituting the index value and the modified weight into the fuzzy mapping function to obtain a quantitative evaluation model of the network-electric efficiency; step 3, under the condition that the index value is known, establishing an inverse problem model for optimizing the index weight by evaluating the power efficiency of the network in the model through a least square method; step 4, applying a regularization to the inverse problem model to suppress the numerical ill-condition, that is, adding a regularization penalty function term to the inverse problem mathematical model; step 5, using Newton-Raphson iterative algorithm to solve the regularized inverse problem model to obtain the optimal weight.
2. The optimization method of network-electric efficiency evaluation model based on the numerical inverse problem according to claim 1, characterized in that in the step 1, extracting indexes related to the network-electric efficiency, establishing an index system for evaluating the efficiency, and setting the weight of each index, specifically as follows: extracting the indicators related to network-electric efficiency, including frequency band utilization rate, channel utilization rate, network capacity, transmission delay, bit error rate, packet loss rate, signal-to-noise ratio, network connectivity, mobility and survivability, establishing an index system k=(k,k,,,k,) for evaluating efficiency, k,k,,---,k, indicate the first to N indicators in sequence, and setting the weights of each index as w, =(w,,w, ,---,w, ) through expert evaluation, and ww, ,---,w, are the weights of the indicators k,k,,,k,.
3. The optimization method of network-electric efficiency evaluation model based on the numerical inverse problem according to claim 1, characterized in that in the step 2, establishing a fuzzy mapping from the evaluation index system to the network-electric efficiency, and using the S-type function to modify the index weight, and substituting the index value and the modified weight into the fuzzy mapping function to obtain a quantitative evaluation model of the network-electric efficiency, specifically as follows: establishing the fuzzy mapping FE=f(k) of the evaluation index system to the network-electric efficiency, and modifying the index weight by S-function, and obtaining the quantitative evaluation model of the network-electric efficiency X 1 B=) ok by substituting the index value and weight into the fuzzy mapping function, where f([) represents the mapping function relationship between the index value and the network efficiency, Æ represents the network-electric efficiency, 4; represents the i-th index quantization value, and w; represents the i-th index weight.
4. The optimization method of network-electric efficiency evaluation model based on the numerical inverse problem according to claim 1, characterized in that in the step 3, under the condition that the index value is known, establishing an inverse problem model for optimizing the index weight by evaluating the power efficiency of the network in the model through a least square method, specifically as follows: under the condition that the index is known, the network-electric efficiency is Yk E=f ENT and the inverse problem model for optimizing the index weight is as follows: N min e(w,) =] 6m) Ef <2 (fi0w)-E)
Wy = (We Wy ew) S00) =o foros) E = (ELE, E,) where e(w,) represents the difference between the calculated efficiency value and the actual accurate efficiency expressed by the least square method; wz represents the index weight vector, and the component w, of wy is the corresponding weight of each index; f(w,) represents the network-electric efficiency calculated by known indicators and weights, and the component f,(w,) of f(w,) isthe efficiency value calculated by each group of indicators; E represents the accurate power efficiency value obtained by simulation or experiment, and the component £ of E is the accurate efficiency value corresponding to each group of indicators; N represents the number of indicators, and m represents the number of simulations or experiments, that is, the number of groups with known indicator values.
5. The optimization method of network-electric efficiency evaluation model based on the numerical inverse problem according to claim 1, characterized in that in the step 4, applying a regularization to the inverse problem model to suppress the numerical ill-condition, that is, adding a regularization penalty function term to the inverse problem mathematical model, specifically as follows: applying the regularization to the inverse problem model to suppress the numerical ill-condition, that is, _ 2 ©) _ yp ON min e(wy) =| fw) —E| tor Low, —w, ) where œ represents a regularization parameter, L represents regularization matrix, s represents iteration times, w,” represents initial index weight and w,“ represents index weight of the s-th iteration.
6. The optimization method of network-electric efficiency evaluation model based on the numerical inverse problem according to claim 1, characterized in that in the step 5, using Newton-Raphson iterative algorithm to solve the regularized inverse problem model to obtain the optimal weight, specifically as follows:
a . LU505180 the iteration format is as follows: -1 Mw = (JI +al'L) [J] (fw) = E)+al Low, ww.) wD =p Oy A ©) where J represents the Jacobian matrix of network-electric efficiency to index weight, f(w,) and Aw, respectively represent the corresponding calculation efficiency value and index weight iteration difference when the iteration number is s, w, “is the index weight value obtained after s-step iteration.
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