CN112444737B - Method for determining fault parameter range of analog circuit - Google Patents
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Abstract
The invention discloses a method for determining a fault parameter range of an analog circuit, which takes element parameter vectors as individuals of a genetic algorithm population, values of parameter values of fault elements are taken in a preset fault value range when an initial population is generated, values of other elements are taken in a tolerance range, and the range of the parameter of the fault element is extracted according to a final generation population after iteration is completed. In the iterative process of the genetic algorithm, two individual optimization modes can be set, and when the individual optimization is carried out, the specific individual optimization modes are adopted according to different individual numbers meeting the requirements of the fitness value, so that the iterative effect is improved. The invention realizes the accurate determination of the parameter range of the fault element through a genetic algorithm.
Description
Technical Field
The invention belongs to the technical field of analog circuit fault diagnosis, and particularly relates to a method for determining a fault parameter range of an analog circuit.
Background
In the working process of the analog circuit, the performance degradation can be caused by the component degradation, and the functional fault can be prevented by estimating the component parameters in time. When the analog circuit is in failure, the parameters of the non-failure elements except the failure element are random numbers within the tolerance range, namely all the parameters of the elements are variables. The number of the test points of the analog integrated circuit is limited, and the number M of the independent test quantities is often far less than the number C of the elements, so that only an underdetermined equation set can be established through the test quantities and the element parameters, and the parameter values of the fault elements cannot be accurately calculated. But can be based on circuit configuration (transfer function) and tolerance ranges And obtaining a possible fault range of the fault parameters. And providing support for circuit performance degradation prediction. Assume that the transfer function h (x) is x1x2，x1、x2Representing the values of the parameters for two elements, with a nominal value of 10 for both elements, the standard output H is 100. The circuit failed, the measured output was 120, and the source of the failure was known to be x1Then x is easily obtained112. Considering a non-faulty element x2Tolerance (tolerance parameter α ∈ [ -0.05, 0.05)]) When x is2X which produces a fault output of 120 at a tolerance lower limit of 9.51Should be 12.6; when x is2X which produces a fault output of 120 at an upper tolerance limit of 10.51Should be 11.4. I.e. x under the influence of a tolerance of + -5%1In a closed interval [11.4,12.6 ]]Any value may result in a fault output of 120. When the circuit structure becomes complicated, the analysis of the closed interval is difficult to calculate accurately, i.e. to determine the fault parameter range.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for determining the fault parameter range of an analog circuit, so as to accurately determine the parameter range of a fault element.
In order to achieve the above object, the method for determining the fault parameter range of the analog circuit comprises the following steps:
s1: obtaining the number C of elements in the analog circuit and the parameter nominal value x of each element jNDetermining a transmission function of the analog circuit at a preset measuring point, and acquiring a fault output voltage Z of the analog circuit at the preset measuring point in the current fault state and a serial number C of a detected fault element, wherein j is 1,2, … and C;
s2: defining the element parameter vector X as [ X ]1,x2,…,xC]As an individual of a genetic algorithm population, generating N individuals to form an initial population P, wherein the specific method comprises the following steps: setting the parameter value x of the faulty element c as desiredcThe value range of the fault, the parameter value x of the fault element c in each individual in the initial population PcTaking values in the fault value range, and taking the parameters x of the other elements jj′Within a tolerance range (x)j′N×(1-α),xj′NX (1+ alpha)) in which x is a numberj′NNominal value of the parameter representing element j', j ═ 1,2, …, C&j′≠c；
S3: initializing the iteration time t as 1;
s4: crossing and varying individuals in the population P to obtain a new population Q, wherein a parameter value x of a fault element c needs to be ensured in the crossing and varying processescTaking values in a fault value range, and taking values of parameter values of non-fault elements in a tolerance range;
s5: merging the population P and the population Q to obtain a merged population S;
s6: respectively calculating the fitness values corresponding to 2N individuals in the combined population S, wherein the calculation method of the individual fitness values comprises the following steps: calculating the output voltage of the element parameter vector corresponding to the individual at a preset measuring point according to the transmission function, then calculating the Euclidean distance between the output voltage and the fault output voltage Z, and taking the Euclidean distance as an individual fitness value, wherein the smaller the fitness value, the better the individual is; selecting N next generation individuals according to the fitness value to form a next generation population P';
S7: judging whether the iteration time t reaches the preset maximum iteration time tmaxIf not, go to step S8, otherwise go to step S9;
s8: returning to step S4 when the population P is equal to P', t is equal to t + 1;
s9: deleting all individuals with fitness value larger than 0.01 xZ from N individuals of the last generation population P', then arranging the rest individuals in ascending order according to the parameter value of the fault element c, wherein the parameter value of the fault element c of the 1 st individual in the obtained individual sequence is the lower limit x of the parameter range of the fault element ccLThe parameter value of the last individual failed component c is the upper limit x of the parameter range of the failed component ccUTo obtain a parameter x determining the faulty component ccRange of [ x ]cL,xcU]。
The method for determining the fault parameter range of the analog circuit takes element parameter vectors as individuals of a genetic algorithm population, when an initial population is generated, the parameter values of fault elements take values in a preset fault value range, the values of other elements take values in a tolerance range, and the range of the fault element parameters is extracted according to the last generation of population after iteration is completed. In the iterative process of the genetic algorithm, two individual optimization modes can be set, and when the individual optimization is carried out, the specific individual optimization modes are adopted according to different individual numbers meeting the requirements of the fitness value, so that the iterative effect is improved. The invention realizes the accurate determination of the parameter range of the fault element through a genetic algorithm.
Drawings
FIG. 1 is a flow chart of an embodiment of a method for determining a fault parameter range of an analog circuit according to the present invention;
FIG. 2 is a circuit diagram of a second order Thomas analog filter circuit in the present embodiment;
FIG. 3 is a distribution diagram of individual fitness values in the population of the generation 2 in the present example;
FIG. 4 is a distribution diagram of individual fitness values in the population of the 101 th generation in the present embodiment;
FIG. 5 is a diagram showing the distribution of fitness values of individuals in the population of the last generation in this embodiment.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
To better explain the technical solution of the present invention, first, the technical idea of the present invention is briefly explained.
Assuming that the circuit transfer function is H (j ω), where j denotes the imaginary unit and ω denotes the angular frequency, it is a function of the element parameter, i.e., H (X), where X denotes the element parameter vector, and X ═ X, at the chosen test frequency1,x2,…,xC]，xjThe parameter of the jth element, j being 1,2, …, C representing the number of elements of the analog circuit, is denoted by x jN. When the parameter of the c-th element drifts to generate a fault, the parameter value exceeds the tolerance rangeEnclose (x)jN×(1-α),xjNX (1+ alpha)) (alpha represents a tolerance parameter, and the value range of the tolerance parameter is within the range of alpha epsilon (0, 0.05)]) Other elements vary randomly within tolerances and can be expressed as follows:
assuming the measured fault output voltage is phasor Z, the faulty element parameter x needs to be foundcAll possible values of (range x)cL,xcU]，0＜xcL＜xcUInfinity, minimizing the following:
where h (X) is an output voltage obtained by calculation according to the transmission function and the element parameter vector X, and it is a phasor having a real part and an imaginary part, | | | | | represents solving a two-norm, that is, a failure element parameter value is determined according to the euclidean distance between the output voltage h (X) and the failure output voltage Z.
Based on the above thought, the method for determining the fault parameter range of the analog circuit is provided. FIG. 1 is a flow chart of an embodiment of a method for determining a fault parameter range of an analog circuit according to the present invention. As shown in fig. 1, the method for determining the fault parameter range of the analog circuit of the present invention specifically includes the following steps:
s101: acquiring analog circuit fault data:
obtaining the number C of elements in the analog circuit and the parameter nominal value x of each elementjNAnd j is 1,2, … and C, determining the transmission function of the analog circuit at the preset measuring point, and acquiring the fault output voltage Z of the analog circuit at the preset measuring point under the current fault state and the serial number C of the detected fault element.
S102: initializing a genetic algorithm population:
defining the element parameter vector X as [ X ]1,x2,…,xC]As an individual of a genetic algorithm population, generating N individuals to form an initial population P, wherein the specific method comprises the following steps:setting the parameter value x of the faulty element c as desiredcThe value range of the fault, the parameter value x of the fault element c in each individual in the initial population PcTaking values in the fault value range, and taking the parameters x of the other elements jj′Within a tolerance range (x)j′N×(1-α),xj′NX (1+ alpha)) in which x is a numberj′NNominal value of the parameter representing element j', j ═ 1,2, …, C&j′≠c。
S103: the number of initialization iterations t is 1.
S104: cross mutation:
crossing and varying individuals in the population P to obtain a new population Q, wherein a parameter value x of a fault element c needs to be ensured in the crossing and varying processescAnd taking values in a fault value range, and taking values of parameter values of non-fault elements in a tolerance range.
In the embodiment, the individual intersection adopts analog binary intersection, the variation adopts polynomial variation, and the intersection rate and the variation rate are set according to actual needs.
S105: merging the populations:
and merging the population P and the population Q to obtain a merged population S, namely S ═ PuQ. Apparently, the pooled population S contains 2N individuals.
S106: the individual preference:
And respectively calculating the fitness values corresponding to 2N individuals in the combined population S. According to the formula (2), the method for calculating the individual fitness value in the invention comprises the following steps: and calculating the output voltage of the element parameter vector corresponding to the individual at a preset measuring point according to the transfer function, then calculating the Euclidean distance between the output voltage and the fault output voltage Z, and taking the Euclidean distance as an individual fitness value, wherein the smaller the fitness value, the better the individual is. And (4) preferably selecting N individuals of the next generation according to the fitness value to form a next generation population P'.
The preferred specific methods for individuals in this example are:
the statistical fitness value is less than or equal to 0.01 x Z | the number of individuals D, Z | representing the modulus of the fault output voltage Z. Individual preference is then divided into two cases according to the individual number D:
and when the number D of the individuals is less than or equal to N, selecting N next-generation individuals from the 2N individuals by adopting a championship alternative method to form a next-generation population P'. The alternative championship is a classic individual preferred method, and the specific steps thereof are not described in detail herein.
When the number D of individuals is larger than N, N individuals of the next generation are selected by adopting an extreme value screening method to form a next generation population P', and the specific method of the extreme value screening method is as follows:
(1) Deleting all individuals with fitness values larger than 0.01 x Z | from the combined population S to obtain a population S ', wherein the number of the individuals of the population S' is D obviously;
(2) and (4) sequencing all the individuals in the population S' in an ascending manner according to the parameter values of the fault element c to obtain an individual sequence.
(3) The first [ N/2] and the last N- [ N/2] individuals are screened from the individual sequence, wherein the [ represents the rounding, namely the middle D-N individuals are deleted, and the N individuals are obtained to form the next generation population P'.
The individual optimization is carried out by adopting the two modes, so that the individuals obtained by optimization can be more reasonable, and the iteration efficiency is improved.
S107: judging whether the iteration time t reaches the preset maximum iteration time tmaxIf not, the process proceeds to step S108, otherwise, the process proceeds to step S109.
S108: let the population P be P', t be t +1, and return to step S104.
S109: determining the parameter range of the fault element:
deleting all individuals with fitness values larger than 0.01 x I Z | from N individuals of the last generation population P', then arranging the rest individuals in an ascending order according to the parameter values of the fault elements c, wherein the parameter value of the fault element c of the 1 st individual in the obtained individual sequence is the lower limit x of the parameter range of the fault element ccLThe parameter value of the last individual failed component c is the upper limit x of the parameter range of the failed component c cUThereby obtaining the parameter x of the fault element ccRange of [ x ]cL,xcU]。
In order to better illustrate the technical scheme and the technical effect of the invention, a specific analog circuit is adoptedThe invention is tested and verified. Fig. 2 is a circuit diagram of a second-order thomas analog filter circuit in the present embodiment. As shown in fig. 2, the second-order thomas analog filter circuit in this embodiment includes 6 resistor elements, 2 capacitors and 3 amplifiers, and the nominal values of the parameters of the elements are as shown in fig. 2. In this example, V isoutAs a measurement point, the transfer function is shown as follows:
in this embodiment, the failure element is set as a resistor R2Let its parameter value be 12k Ω, and the other components be in the tolerance range (if the tolerance parameter α is set to 0.05 in this embodiment, the tolerance range is (x)jN×95％,xjNX 105%)). The parameter values for all elements are: r1＝9965Ω，R2＝12000Ω，R3＝9991Ω，R4＝9933Ω，R5＝9967Ω，R6＝9929Ω，C1＝10.04nF，C210.08 nF. The input signal is a sinusoidal signal with the effective value of 1V and the frequency of 1 KHz. The simulation results in that the fault voltage phasor response Z is 0.9484-0.8283iV, wherein i is an imaginary unit.
Defining the element parameter vector X as [ X ]1,x2,,xC]In this example, C is 8, the first 6 bits are resistance, and the last 2 bits are capacitance, which are individuals of the genetic algorithm population. Setting the faulty element 2 (i.e. resistor R) 2) Parameter value x ofcFault value range of [1 Ω,100m Ω ]]The parameter value of the fault element 2 in each individual in the initial population P randomly takes a value in the fault value range, and the parameters x of the other elements j' are randomly taken valuesj′Within a tolerance range (x)j′N×(1-α),xj′NX (1+ α)) are randomly selected. Setting the number of the population N as 100 and the maximum iteration time tmax＝400。
And then, simulating binary intersection and polynomial variation, combining the parent and the generated new population to obtain a combined population S, and then calculating the fitness values of all individuals in the combined population S. Table 1 is a list of element parameter vectors and fitness values corresponding to some individuals in the first generation pooled population.
TABLE 1
The number of individuals having fitness values of 0.01 x Z | or less in the first generation pooled population is small, less than 100, and therefore the next generation is preferably generated using tournaments. FIG. 3 is a graph showing the distribution of fitness values of individuals in the population of the 2 nd generation in this example. The abscissa in fig. 3 represents the parameter values of the faulty component 2 in the respective individual component parameter vectors, and the ordinate represents the corresponding fitness value.
Table 2 is a list of element parameter vectors and fitness values corresponding to the first 10 individuals with the largest parameter value and the first 10 individuals with the smallest parameter value of the faulty element 2 in the population of the 100 th generation.
TABLE 2
FIG. 4 is a distribution diagram of individual fitness values in the population of the 101 th generation in this example. As shown in fig. 4, the parameter values of the faulty element 2 in the individual individuals in the 101 th generation population have exhibited a bipolar differentiation situation, and the minimum and maximum values of the parameter values of the faulty element 2 in the individual with an adaptation value of 0.01 × | Z |, are 11660 Ω and 12383 Ω, respectively.
FIG. 5 is a diagram showing the distribution of fitness values of individuals in the population of the last generation in this embodiment. In the last generation population, all individuals with fitness values larger than 0.01 x Z are deleted, and then the rest individuals are arranged in ascending order according to the parameter values of the fault element 2, so that the lower limit x of the parameter range of the fault element 2 can be obtained2L11.611k Ω, upper limit x of the parameter range of the faulty component 22U12.505k Ω. I.e. the parameter values of all faulty components 2In the closed interval [11.611k Ω,12.505k Ω]The internal faults can generate fault voltage Z which is 0.9484-0.8283 iV. Obviously, a set fault R2Also within this range is 12k Ω.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.
Claims (2)
1. A method for determining the fault parameter range of an analog circuit is characterized by comprising the following steps:
s1: obtaining the number C of elements in the analog circuit and the parameter nominal value x of each elementjNDetermining a transmission function of the analog circuit at a preset measuring point, and acquiring a fault output voltage Z of the analog circuit at the preset measuring point in the current fault state and a serial number C of a detected fault element, wherein j is 1,2, … and C;
s2: defining the element parameter vector X as [ X ]1,x2,…,xC]As an individual of a genetic algorithm population, generating N individuals to form an initial population P, wherein the specific method comprises the following steps: setting the parameter value x of the faulty element c as desiredcThe value range of the fault, the parameter value x of the fault element c in each individual in the initial population PcTaking values in the fault value range, and taking the parameters x of the other elements jj′Within a tolerance range (x)j′N×(1-α),xj′NX (1+ alpha)) in which x is a numberj′NNominal value of the parameter representing element j', j ═ 1,2, …, C&j '≠ C j ═ 1,2, …, C and j' ≠ C, α denotes tolerance parameter whose range α ∈ (0, 0.05.]；
S3: initializing the iteration time t as 1;
s4: crossing and varying individuals in the population P to obtain a new population Q, wherein a parameter value x of a fault element c needs to be ensured in the crossing and varying processes cTaking values in a fault value range, and taking values of parameter values of non-fault elements in a tolerance range;
s5: merging the population P and the population Q to obtain a merged population S;
s6: respectively calculating the fitness values corresponding to 2N individuals in the combined population S, wherein the calculation method of the individual fitness values comprises the following steps: calculating the output voltage of the element parameter vector corresponding to the individual at a preset measuring point according to the transmission function, then calculating the Euclidean distance between the output voltage and the fault output voltage Z, and taking the Euclidean distance as an individual fitness value, wherein the smaller the fitness value, the better the individual is; selecting N next generation individuals according to the fitness value to form a next generation population P';
s7: judging whether the iteration time t reaches the preset maximum iteration time tmaxIf not, go to step S8, otherwise go to step S9;
s8: returning to step S4 when the population P is equal to P', t is equal to t + 1;
s9: deleting all individuals with fitness values larger than 0.01 x I Z | from N individuals of the last generation population P', then arranging the rest individuals in an ascending order according to the parameter values of the fault elements c, wherein the parameter value of the fault element c of the 1 st individual in the obtained individual sequence is the lower limit x of the parameter range of the fault element c cLThe parameter value of the last individual failed component c is the upper limit x of the parameter range of the failed component ccUThereby obtaining the parameter x of the fault element ccRange of [ x ]cL,xcU]。
2. The analog circuit fault parameter range determination method according to claim 1, wherein in step S6, the following method is preferably adopted by the individual:
counting the number D of individuals with a fitness value less than or equal to 0.01 x Z, wherein Z represents the modulus of the fault output voltage Z; when the number D of individuals is less than or equal to N, selecting N next-generation individuals from the 2N individuals by adopting a championship two-out method to form a next-generation population P'; when the number D of individuals is larger than N, N individuals of the next generation are selected by adopting an extreme value screening method to form a next generation population P', and the specific method of the extreme value screening method is as follows:
(1) deleting all individuals with fitness values larger than 0.01 x Z | from the combined population S to obtain a population S';
(2) arranging all individuals in the population S' in an ascending order according to the parameter values of the fault elements c to obtain individual sequences;
(3) the first [ N/2] and the last N- [ N/2] individuals are screened from the individual sequence, and the [ represents the integer ] to obtain N individuals to form the next generation population P'.
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