Key pvt angle evaluation method, device and equipment based on probability integral transform

Abstract

The application provides a key PVT corner evaluation method and device based on probability integral transformation and equipment. The method comprises the following steps: simulating N design samples randomly sampled to obtain a performance index vector to form an original data set S; modeling the performance index vector of each PVT corner by using a kernel density estimation method to obtain a probability density function and a cumulative distribution function of a circuit performance parameter; mapping the performance index vector into a standard normal distribution variable through a probability integral transformation; constructing a multivariate Gaussian distribution model based on the mapped data and obtaining new samples, combining the new samples with the original data set S to form a complete data set, counting the frequency of each corner as the worst PVT corner in the complete data set, and sorting the frequency to obtain a key PVT corner set, wherein the highest frequency is the first key PVT corner. The embodiment of the application can simplify simulation calculation, significantly reduce the calculation cost, accurately lock the PVT corner with the greatest impact on the circuit performance, and improve the design reliability.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of integrated circuit design, and in particular to a key PVT corner evaluation method and device based on probability integral transformation. BACKGROUND

[0002] Under the background of integrated circuit (IC) design and manufacturing continuously advancing towards advanced process nodes, the fluctuations of process, voltage, and temperature (PVT) have an increasingly significant impact on circuit performance, power consumption, and reliability. These parameter changes, which are derived from the manufacturing process and working environment, can cause the circuit to perform sub-optimally or even fail in actual applications. Therefore, accurately identifying and evaluating the worst case of each performance parameter of the circuit under different PVT corners (PVT Corner), i.e., the PVT corner with the worst performance parameter of the circuit, to determine the reliable lower limit of the performance parameter, is crucial for ensuring the robustness and yield of the chip under complex operating conditions. This analysis aims to help engineers foresee potential risks at an early stage of design, thereby optimizing the design and ensuring that the product maintains high performance standards during mass production and long-term use.

[0003] In the integrated circuit design flow, the traditional PVT analysis uses the exhaustive method to find the worst corner of the circuit performance indicators. Usually, it needs to complete the circuit simulation under all PVT corners to identify the worst performance PVT corner. However, as the process node enters the advanced process, the exhaustive method is facing severe challenges. The diversity of device types, the complexity of multi-power modes, RC parasitic changes and other factors significantly expand the spatial dimension of the PVT corners that need to be considered in circuit design, leading to an exponential increase in the number of simulations required by the exhaustive method, resulting in great resource consumption. To overcome the limitations of traditional methods, the industry has proposed modeling methods such as linear response surface models to reduce the number of simulations, but such models are difficult to accurately describe nonlinear effects and are very likely to miss the real worst corner, with poor reliability. The Fast PVT method uses Gaussian process models (GPM) and model building optimization (MBO) to obtain a higher reliability performance model through multiple simulation iterations to estimate the worst PVT corner of the circuit performance. Due to its stronger nonlinear modeling capability, the Fast PVT method can effectively improve the accuracy of identifying the key PVT corner of a given circuit design while reducing simulation costs. However, whether it is a linear response surface model method or a Fast PVT method, the goal is to find the worst corner from hundreds or thousands of PVT corners using as few simulations as possible for a specific circuit design. Once the circuit design parameters change, the complete PVT analysis process needs to be repeated, and there is a lack of adaptability to design parameter changes. Due to the lack of response capability of existing methods to design space changes, the worst PVT corner analysis process will be repeated multiple times in the process of iterating circuit design parameters, significantly increasing the computational cost and design cycle.

[0004] [1] McConaghy T, Breen K, Dyck J, et al. Variation-aware design ofcustom integrated circuits: a hands-on field guide[M]. Springer Science&Business Media, 2012. DOI 10.1007 / 978-1-4614-2269-3 SUMMARY

[0005] The purpose of the present application is to provide a key PVT corner evaluation method, device and equipment based on probability integral transformation, which solves the problems of high simulation cost, low accuracy and inability to adapt to design parameter iteration in high-dimensional PVT corner space in the existing PVT corner evaluation method.

[0006] To address the aforementioned technical problems, this application provides a key PVT angle evaluation method based on probability integral transformation, comprising: simulating N randomly sampled design samples at each PVT angle to obtain performance index vectors; all performance index vectors constituting an original dataset S; modeling the performance index vectors at each PVT angle using kernel density estimation to obtain the probability density function and cumulative distribution function of circuit performance parameters; mapping the performance index vectors to standard normal distribution variables through probability integral transformation; constructing a multivariate Gaussian distribution model based on the mapped data; obtaining new samples based on the multivariate Gaussian distribution model, calculating the cumulative distribution probability of each new sample at each PVT angle, and mapping the new samples to the original circuit performance space through inverse transformation to obtain the original circuit performance of the new samples at the PVT angle; and combining the new samples with the original dataset S to form a complete dataset. Define the worst PVT angle Indexes, statistical data sets Each corner is considered the worst PVT corner. The frequency of each angle is used to sort the key PVT angles, and the angle with the highest frequency is the first key PVT angle.

[0007] Optionally, the worst PVT angle The index is defined as:

[0008] where n∈{1,2,…,N+N} new}in, This represents the circuit performance parameters, where K is the number of PVT angles, k represents a specific PVT angle, and N is the number of samples in the original dataset S. This represents the number of new samples.

[0009] Optionally, the probability density function The expression is:

[0010] , where g( ) is the kernel function. Let y represent the bandwidth at the k-th PVT angle, and y represent the circuit performance parameters. This represents the circuit performance parameters at the nth sampling point and the kth PVT angle;

[0011] The cumulative distribution function The expression is: .

[0012] Optionally, the kernel function It is one of the Gaussian kernel, Epanechnikov kernel, or uniform kernel, said The calculation method is as follows:

[0013] wherein, is the absolute median deviation of all performance index parameters in the original data set S under the kth PVT corner, and N is the number of samples in the original data set S.

[0014] Optionally, the mapping of the performance index vector into a standard normal distribution variable through a probability integral transformation comprises: calculating the circuit performance parameter the probability of occurrence ,

[0015] ; wherein, the probability is mapped to a standard normal distribution space using an inverse function of a standard normal distribution cumulative distribution function.

[0016] Optionally, a multivariate Gaussian distribution model is constructed based on the mapped data, comprising: a K-dimensional vector formed by the mapped data

[0017] { ,

[0018] The Gaussian distribution model is represented as: ; wherein, is a covariance matrix, represented as ; I is an identity matrix, represents a sample covariance matrix,

[0019] , a hyperparameter .

[0020] Optionally, the hyperparameter λ is determined through cross-validation, specifically comprising:

[0021] dividing a sample set into P non-overlapping subsets; dividing the subsets, selecting a single subset as a test set and the rest as a training set, a total of P divisions; for each division, based on all sampling points in the training set, calculating the hyperparameter covariance according to the covariance matrix formula; calculating the likelihood function of each sampling point in the test set under different λ values according to the covariance, and summing up the total on different division test sets, selecting as the optimal value.

[0022] Optionally, the method further comprises: selecting the first r key PVT corners to construct an index set , and the rest of the key PVT corners to construct a candidate set , calculating the candidate set The PVT angle with the highest coverage is selected as the (r+1)th key PVT angle, and the (r+1)th key PVT angle is updated in the index set. In the process, calculate the updated set of indices. The coverage rate, up to the updated index set. Able to cover the sample set The worst PVT angle among all samples .

[0023] Optionally, the coverage The calculation formula is: ,in, Let K be the indicator function, and K be the number of PVT angles. hour Otherwise, it is 0; N is the number of samples in the original dataset S. The number of new samples; the (r+1)th critical PVT angle is determined by the following formula: , It represents a specific PVT angle.

[0024] This application embodiment also provides a key PVT angle evaluation device based on probability integral transformation, including: an original dataset S construction module, used to simulate N randomly sampled design samples under each PVT angle to obtain performance index vectors, and all performance index vectors constitute the original dataset S;

[0025] The kernel density estimation modeling module is used to model the performance index vector of each PVT angle using the kernel density estimation method to obtain the probability density function and cumulative distribution function of the circuit performance parameters.

[0026] The mapping module is used to map the performance index vector to a standard normally distributed variable through probability integral transformation;

[0027] The Gaussian distribution model building module is used to construct a multivariate Gaussian distribution model based on the mapped data.

[0028] The inverse transformation module is used to obtain new samples based on the multivariate Gaussian distribution model, calculate the cumulative distribution probability of each new sample under each PVT angle, and map the new samples to the original circuit performance space through inverse transformation to obtain the original circuit performance of the new samples under the PVT angle.

[0029] The key PVT angle evaluation module is used to combine the new sample with the original dataset S to form a complete dataset. Define the worst PVT angle Indexes, statistical data sets Each corner is considered the worst PVT corner. The frequencies of the PVT angles are counted, and the key PVT angle set is obtained by frequency sorting, wherein the PVT angle with the highest frequency is the first key PVT angle.

[0030] The embodiment of the present application further provides an electronic device, including a processor, a memory, and a computer program stored in the memory and capable of running on the processor, and the processor implements the steps of the key PVT angle evaluation method based on probability integral transformation when the computer program is executed.

[0031] The embodiment of the present application significantly reduces the simulation times and the calculation cost through a small amount of sampling and statistical modeling. The kernel density estimation and the covariance regularization are introduced to improve the model accuracy and robustness. Based on the multivariate Gaussian modeling and the coverage rate recursive optimization, a limited number of key angles are locked from hundreds of PVT angles, the real worst working condition is avoided to be missed, the PVT angle with the greatest impact on the circuit performance is accurately locked, and the design reliability is improved. The covariance regularization and the cross-validation mechanism make the model have the automatic adaptation capability of design parameter iteration, the full-process analysis does not need to be repeated when the process is changed, the design cycle is shortened, and the optimization efficiency is improved. BRIEF DESCRIPTION OF DRAWINGS

[0032] One or more embodiments are illustrated by way of example with reference to the drawings, which are not limiting of the embodiments and which are merely meant to explain the embodiments. The reference numbers in the drawings indicate like reference numbers and elements, unless otherwise indicated. The drawings in the accompanying drawings are not to scale and are merely meant to explain the embodiments.

[0033] Figure 1 is a flowchart of a key PVT angle evaluation method based on probability integral transformation according to an embodiment of the present application;

[0034] Figure 2 is a flowchart of a key PVT angle evaluation method based on probability integral transformation according to another embodiment of the present application;

[0035] Figure 3 is a structural schematic diagram of a key PVT angle evaluation device based on probability integral transformation according to an embodiment of the present application;

[0036] Figure 4 is a structural schematic diagram of a key PVT angle evaluation device based on probability integral transformation according to another embodiment of the present application;

[0037] Figure 5 is a structural schematic diagram of an electronic device according to an embodiment of the present application. DETAILED DESCRIPTION

[0038] The following detailed description is presented in terms of specific embodiments illustrating the applications. These descriptions and examples are provided as disclosure of the applications and are not intended to limit the scope of the applications. Furthermore, various omissions of structure and / or detail are done for the sake of clarity and conciseness and are not intended to limit the scope of the applications. Those skilled in the art will understand that the applications are capable of use in other contexts and with many modifications of structure and equivalent apparatus. Many embodiments of the applications are described in terms of steps or functions.

[0039] It should be noted that various aspects of the embodiments described below are presented in terms of sequences of actions within a process. The description and examples illustrating the aspects are intended to provide a description of the aspects, and not to limit the scope of the aspects. One of ordinary skill in the art will recognize that the aspects described herein can be carried out under a variety of other conditions and / or with a variety of other processes in addition to those described herein. In other words, one of ordinary skill in the art will recognize that the aspects described herein can be carried out under a variety of other conditions and / or with a variety of other processes in addition to those described herein.

[0040] It should also be noted that the graphical illustrations provided in the following embodiments are merely schematic and generally only show components that are pertinent to the present application, and are not drawn to scale, in terms of the number, shape and size of the components, as actually implemented, which can be a matter of design choice, and can be more complex in layout, as well as in terms of the components' shapes, numbers and proportions.

[0041] In addition, in the following description, numerous specific details are set forth in order to provide a thorough understanding of the examples. However, it will be recognized by one of ordinary skill in the art that the various embodiments can be practiced without these specific details.

[0042] In current integrated circuit design practice, especially in frequent design parameter iteration optimization, a key problem to be solved is how to quickly and accurately identify the key PVT corner in which the circuit performance is worst in a large number of PVT corners and a wide range of design parameter space with extremely low calculation cost. The traditional exhaustive method or modeling method is not competent in dealing with this demand due to high simulation cost and low adaptability under new design parameters. Therefore, the industry urgently needs an innovative fast PVT analysis technology that can effectively predict and screen out the key PVT corner with the worst circuit performance in the entire design parameter space by only sampling a small number of points, allowing designers to focus on optimizing circuit performance under these key PVT conditions to improve the efficiency of design iteration.

[0043] The inventors of the present application found that, assuming that the design parameters of a given circuit can be represented by an M-dimensional vector characterizing, where each represents an independent design parameter, such as the width, length, capacitance value, resistance value, etc. of a transistor. These design parameters satisfy independent uniform distribution. It is assumed that a total of K PVT corners need to be considered in the design process , where each represents a specific PVT corner. For a given PVT corner , a certain circuit performance parameter can be represented as a function . It is assumed that the larger the value of , the worse the circuit performance. For any given design parameter x, the index of the worst PVT corner can be defined as:

[0044] ,

[0045] Let X represent the legal value range of the design parameter x, then the value range of the design parameter x when the kth PVT corner becomes the worst corner can be calculated.

[0046] .

[0047] The larger the value of , the more likely it is that the circuit performance will deteriorate at the kth PVT corner , and the higher the probability that the PVT corner becomes the worst PVT corner. The purpose of the present application is to quickly determine the PVT corner with the highest probability of becoming the worst corner in the entire design parameter space, i.e. the key PVT corner, by sampling and simulating as few times as possible.

[0048] Based on this, embodiments of this application provide a method for evaluating key PVT angles based on probability integral transformation, the process of which is as follows: Figure 1 As shown, the details are as follows:

[0049] In step 101, under each PVT angle, simulations are performed on N randomly sampled design samples to obtain performance index vectors. All performance index vectors constitute the original dataset S. Specifically, random sampling can be performed within the legal value range to obtain N design sample points. , where n is a design sample point. At each PVT angle Next, simulations are performed on all sample points to obtain the performance index vector. k represents a PVT angle, and the performance index vector. Each vector in the vector represents a circuit performance parameter. By taking k=1,2,...,K respectively, we obtain the simulation results of sample points under all PVT angles and construct a dataset. .

[0050] In step 102, the performance index vector for each PVT angle is modeled using the kernel density estimation method to obtain the probability density function and cumulative distribution function of the circuit performance parameters. Specifically, at each PVT angle... Down, K represents the number of PVT angles, and the kernel density estimation method is used to estimate the performance index vector. Modeling is performed to obtain the k-th PVT angle. Lower circuit performance parameters probability density function .

[0051] probability density function The expression is:

[0052] (1)

[0053] in, It's a kernel function. Let y represent the bandwidth at the k-th PVT angle, and y represent the circuit performance parameters. This represents the circuit performance parameters at the nth sampling point and the kth PVT angle; the kernel function g( in the embodiments of this application) It can be one of the Gaussian kernel, Epanechnikov kernel, or uniform kernel. It can be determined using the following calculation method:

[0054] ,in, Let be the absolute median difference of all performance index parameters in the original dataset S under the k-th PVT angle, and N be the number of samples in the original dataset S.

[0055] Cumulative distribution function The expression is: (2)

[0056] In this step, we can assume performance index vectors under different PVT angles. These are independent of each other; we will not consider the circuit performance parameters of the same circuit under different PVT angles for now. The correlation.

[0057] In step 103, the performance index vector is mapped to a standard normally distributed variable through probability integral transformation. In this step, the circuit performance parameters of the nth design sample can be calculated first. The probability of occurrence is calculated, and the probability is mapped to the standard normal distribution space using the inverse function of the cumulative distribution function of the standard normal distribution.

[0058] Specifically, the nth design sample at the kth PVT angle can be calculated using the formula (2) above. Circuit performance parameters probability of occurrence ;

[0059] in,

[0060] According to the principle of probability integral transformation, random variables It follows a uniform distribution on the interval [0, 1].

[0061] Then, using the inverse function of the cumulative distribution function of the standard normal distribution. ,Will Mapping to the standard normal distribution space, we get:

[0062] (3)

[0063] in,{ } is a random variable that follows a standard normal distribution (i.e., a Gaussian distribution with a mean of 0 and a variance of 1). This indicates the circuit performance parameters The values ​​obtained by mapping the original circuit performance parameter space to the standard normal distribution space.

[0064] In step 104, a multivariate Gaussian distribution model is constructed based on the mapped data. Specifically, the circuit performance parameters under all PVT angles are transformed and mapped based on steps 102 and 103, and are then represented by a K-dimensional vector {...}. , the K-dimensional vector satisfies the following high-dimensional Gaussian distribution: (4)

[0065] where, is the covariance matrix, denoted as (5)

[0066] I is the unit matrix;

[0067] denotes the sample covariance matrix, (6)

[0068] hyperparameter .

[0069] wherein the hyperparameter λ can be determined by a cross-validation (CV) method to determine its optimal value. The specific steps are as follows:

[0070] The sample set is divided into P non-overlapping subsets;

[0071] The subsets are divided, and a single subset is selected as the test set, and the rest is the training set, a total of P divisions;

[0072] For each division, based on all the sampling points in the training set, the covariance of the hyperparameter λ is calculated according to the covariance matrix formula;

[0073] According to the covariance, the likelihood function of each sampling point in the test set under different λ values is calculated, and the sum is summed on different division test sets, and the λ that makes the sum of the likelihood value maximum is selected as the optimal value.

[0074] Specifically, the sample set is composed of all K-dimensional vectors . First, the sample set is evenly divided into P non-overlapping subsets . Assume that the value of the hyperparameter λ can be taken as follows: . For each possible value , let be the test set, and all other subsets except the test set constitute the training set . Using a method similar to formula (6), based on all the sampling points in the training set , the sample covariance matrix is calculated. Then according to formula (5), the covariance when the hyperparameter is calculated: I.(7)

[0075] Then, assuming the test set the sampling points in the set satisfy a high-dimensional Gaussian distribution with mean 0 and variance The test set The log of the likelihood function of each sampling point in the test set is calculated and summed up:

[0076] (8)

[0077] In this embodiment, is the probability density function of a high-dimensional Gaussian distribution with mean 0 and variance The corresponding of each subset is accumulated, and the total likelihood value at the time of the hyperparameter is obtained.

[0078] Finally, the that maximizes the total likelihood value is selected as the optimal value of :

[0079] , (9)

[0080] Substitute the optimal value of into equation (6), and we obtain the optimal covariance matrix:

[0081] , (10)

[0082] In step 105, based on the multivariate Gaussian distribution model, new samples are obtained, and the cumulative distribution probability of each new sample at each PVT angle is calculated.

[0083] Specifically, first, based on all sampling points (i.e., N design sample points), the sampling mean of the performance indicator is calculated:

[0084] (11)

[0085] Then, based on a high-dimensional Gaussian distribution with mean and variance , sampling is performed to obtain new samples

[0086] , where j represents a new sample, and K is the number of PVT angles.

[0087] At any given PVT angle , these new samples theoretically satisfy a standard normal distribution with mean 0 and variance 1. Based on this theory, the cumulative distribution probability of each new sample at each PVT angle can be calculated: ​

[0088] (12)

[0089] in It is the cumulative distribution function of the standard normal distribution.

[0090] In step 106, the new sample is mapped to the original circuit performance space through an inverse transformation to obtain the original circuit performance of the new sample at the PVT angle. Specifically, the cumulative distribution function can be estimated using the kernel density in formula (2). inverse function ,Will Mapping to the original circuit performance space, we obtain the j-th new sampling point at the PVT angle. The original circuit performance is as follows:

[0091] (13)

[0092] In step 107, the new sample is combined with the original dataset S to form a complete dataset. Define the worst PVT angle Indexes, statistical data sets Each corner is considered the worst PVT corner. The frequency of each angle is used to sort the key PVT angles, and the angle with the highest frequency is the first key PVT angle.

[0093] Specifically, all newly generated samples in this embodiment can be represented as:

[0094] Together with the original dataset S, they constitute a complete dataset. .

[0095] In an alternative embodiment, for Performance parameters of each sample within Define the worst PVT angle The index is:

[0096] (14)

[0097] in

[0098] This represents the circuit performance parameters, where K is the number of PVT angles and N is the number of samples in the original dataset S. This represents the number of new samples.

[0099] Statistical analysis of each PVT angle Frequency of being selected as the worst angle The most frequent of these is the first critical PVT corner.

[0100] Compared with the prior art, the embodiment of the application firstly performs kernel density estimation on the performance simulation results under each PVT angle respectively, and maps the original performance data to a standard Gaussian distribution space by using a probability integral transformation. Subsequently, a multivariate Gaussian distribution model is constructed in the standard space, and a weighted combination of a sample covariance matrix and a unit matrix is used for regularized covariance estimation, wherein a regularization coefficient is determined by cross-validation. Then, new simulation performance samples are obtained by sampling from the constructed multivariate Gaussian distribution, and are restored to the original performance space by inverse transformation, thereby effectively expanding the sample size.

[0101] For the problem of evaluating key PVT angles in the design parameter space, only a small number of sampling points need to be taken in the entire design parameter space, and a mapping relationship between the original performance distribution and the standard Gaussian space is constructed according to kernel density analysis and probability integral transformation, so that the key PVT angles with the worst circuit performance can be effectively predicted and screened, and the circuit verification efficiency is significantly improved. Meanwhile, the method also introduces a covariance regularization and cross-validation mechanism, which effectively improves the model accuracy, reliability and robustness, so that a small-scale key PVT angle set can be efficiently and reliably screened from a large number of PVT angles.

[0102] The covariance regularization and cross-validation mechanism enables the model to automatically adapt to design parameter iteration, so that the full-process analysis does not need to be repeated when the process is changed, the design cycle is shortened, and the optimization efficiency is improved.

[0103] The embodiment of the application also provides another key PVT angle evaluation method based on probability integral transformation, as shown in Figure 2 , which is optimized on the basis of the embodiment shown in Figure 1 . The optimization is that, after the key PVT angles are screened out, the embodiment of the application further recursively screens the key PVT angles and dynamically optimizes the coverage, further reduces redundant calculation, accurately locks the PVT angle with the greatest impact on the circuit performance, and improves the design reliability. The flow of the key PVT angle evaluation method based on probability integral transformation of the embodiment is as shown in Figure 2 , and is specifically as follows:

[0104] The steps 201-207 of the embodiment are similar to the steps 101-107 of the embodiment shown in Figure 1 , and will not be described here.

[0105] In step 208, the first r key PVT angles are selected to construct an index set , and the remaining key PVT angles are used to construct a candidate set , and the candidate set The PVT angle with the highest coverage is selected as the (r+1)th key PVT angle, and the (r+1)th key PVT angle is updated in the index set. In this embodiment, the first r key PVT angles are selected to construct an index set. It can be represented as For each PVT angle that was not selected as a critical angle Construct candidate set For candidate set Calculate the coverage of all samples. The calculation formula is:

[0106] (15)

[0107] Among them, I( ) is the indicator function, K is the number of PVT angles, when hour Otherwise, the value is 0; N is the number of samples in the original dataset S. This represents the number of new samples.

[0108] Then, the PVT angle with the highest coverage is taken as the (r+1)th critical PVT angle, which is determined by the following formula:

[0109] (16)

[0110] make Update r = r + 1. It represents a specific PVT angle.

[0111] In step 209, the updated index set is calculated. The coverage rate, up to the updated index set. Able to cover the sample set The worst PVT angle among all samples .

[0112] Specifically, the updated index set can be calculated using formula (15). To determine the coverage, repeat step 208 until the current critical PVT corner index set is reached. Able to cover the sample set The worst PVT angle among all samples.

[0113] This embodiment, after identifying critical PVT corners, recursively calculates the worst-case corner coverage for each PVT corner set based on expanded sample data, extracts the critical PVT corner set, and ranks the PVT corners according to their criticality. This further reduces redundant calculations, accurately identifies the PVT corners that have the greatest impact on circuit performance, and improves design reliability.

[0114] Based on the same inventive concept, this application also provides a critical PVT angle evaluation device based on probability integral transformation. It should be noted that the device illustrated below is an example of a device corresponding to one of the above method embodiments, while in other device embodiments, the functions and number of unit modules can be set accordingly based on the aforementioned method embodiments.

[0115] like Figure 3 As shown, the key PVT angle evaluation device based on probability integral transformation includes:

[0116] The original dataset S is constructed by module 1, which is used to simulate N randomly sampled design samples under each PVT angle to obtain performance index vectors. All performance index vectors constitute the original dataset S.

[0117] Kernel density estimation modeling module 2 is used to model the performance index vector of each PVT angle using the kernel density estimation method to obtain the probability density function and cumulative distribution function of the circuit performance parameters;

[0118] Mapping module 3 is used to map the performance index vector to a standard normally distributed variable through probability integral transformation;

[0119] Gaussian distribution model building module 4 is used to build a multivariate Gaussian distribution model based on the mapped data;

[0120] Inverse transformation module 5 is used to obtain new samples based on the multivariate Gaussian distribution model, calculate the cumulative distribution probability of each new sample under each PVT angle, and map the new samples to the original circuit performance space through inverse transformation to obtain the original circuit performance of the new samples under the PVT angle.

[0121] The key PVT angle evaluation module 6 is used to combine the new sample with the original dataset S to form a complete dataset. Define the worst PVT angle Indexes, statistical data sets Each corner is considered the worst PVT corner. The frequency of each angle is used to sort the key PVT angles, and the angle with the highest frequency is the first key PVT angle.

[0122] like Figure 4 As shown, this application embodiment also provides a critical PVT angle evaluation device based on probability integral transformation. This embodiment... Figure 3 The embodiment shown is an improvement, in that the device in this embodiment further includes a key PVT corner set construction and update module 7 and a coverage calculation module 8.

[0123] The data set construction and update module 7 is configured to select the first r key PVT angles to construct an index set , and update the (r+1)th key PVT angle to the index set .

[0124] The coverage calculation module 8 is configured to calculate the PVT angle with the maximum coverage in the candidate set as the (r+1)th key PVT angle, and calculate the coverage of the updated index set , until the updated index set can cover the worst PVT angle of all samples in the sample set . .

[0125] After the key PVT angle evaluation module 6 screens the key PVT angle, the data set construction and update module 7 and the coverage calculation module 8 are further used to recursively screen the key PVT angle and dynamically optimize the coverage, so as to further reduce the redundant calculation, accurately lock the PVT angle with the greatest impact on the circuit performance, and improve the design reliability.

[0126] As shown in Figure 5 , the present application further provides an electronic device, which includes a processor 11, a memory 12, and a computer program stored in the memory 12 and capable of running on the processor 11, and the processor 11 implements the steps of the key PVT angle evaluation method based on the probability integral transformation when executing the computer program.

[0127] The electronic device in the embodiments of the present application includes at least one processor 11 and a memory 12 in communication connection with the at least one processor 11, Figure 5 and one processor 11 is taken as an example for illustration.

[0128] The electronic device can further include an input device 13 and an output device 14.

[0129] The processor 11, the memory 12, the input device 13 and the output device 14 can be connected through a bus or other means, Figure 5 and the connection through the bus is taken as an example.

[0130] The memory 12 is a non-transient computer readable storage medium, which can be used to store non-transient software programs, non-transient computer executable programs and modules, such as the program instructions / modules (for example, the program instructions / modules for implementing the key PVT angle evaluation method based on the probability integral transformation in the embodiments of the present application) corresponding to the key PVT angle evaluation method based on the probability integral transformation in the embodiments of the present application. Figure 3 ​the original data set S construction module 1, the kernel density estimation modeling module 2, the mapping module 3, the Gaussian distribution model construction module 4, the inverse transform module 5, etc.). The processor 11 performs various functional applications and data processing of the server by running the non-transitory software programs, instructions and modules stored in the memory 12, i.e. implements the key PVT angle evaluation method based on the probability integral transform in the above method embodiments.

[0131] The memory 12 can include a program storage area and a data storage area, wherein the program storage area can store an operating system and application programs required by at least one function; the data storage area can store data created by the use of the processing device operating according to the list items, etc. In addition, the memory 12 can include a high-speed random access memory, and can also include a non-transitory memory, such as at least one disk storage device, a flash memory device, or other non-transitory solid-state memory device. In some embodiments, the memory 12 can optionally include a memory disposed remotely with respect to the processor 11, which can be connected to the processor 11 for the key PVT angle evaluation method based on the probability integral transform through a network. Examples of the above network include but are not limited to the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0132] The input device 13 can receive inputted digital or character information, and generate key signal inputs related to user settings and function controls of the processing device operating according to the list items. The output device 14 can include a display device such as a display screen.

[0133] In the present embodiment, when one or more modules stored in the memory 12 are executed by the one or more processors 11, the processor 11 performs the key PVT angle evaluation method based on the probability integral transform in any of the above method embodiments.

[0134] The above product can perform the method provided by the embodiments of the present application, and has the corresponding functional modules and beneficial effects of performing the method. Technical details not described in detail in the present embodiment can be referred to the method provided by the embodiments of the present application.

[0135] The electronic device of the embodiments of the present application exists in various forms, including but not limited to:

[0136] (1) Mobile communication device: the feature of such a device is to have a mobile communication function, and to provide voice and data communication as the main target. Such terminals include: smart phones (such as iPhone), multimedia phones, functional phones, and low-end phones, etc.

[0137] (2) Ultra-mobile personal computer devices: These devices are in the category of personal computers, have computing and processing capabilities, and generally have mobile Internet capabilities. These devices include PDAs, MIDs, and UMPC devices, such as the iPad.

[0138] (3) Portable entertainment devices: These devices can display and play multimedia content. This category includes audio and video players (e.g., iPod), handheld game consoles, electronic books, and smart toys and portable car navigation devices.

[0139] The technical features of the above-described embodiments can be combined in any manner. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described, but it should be understood that any combination of the technical features is within the scope of the present disclosure, as long as the combination does not result in a contradiction.

[0140] The above-described embodiments only express several implementation manners of the present application, and the description is specific and detailed, but it should not be understood as a limitation on the patent scope of the application. It should be pointed out that, for those skilled in the art, some modifications and improvements can be made without departing from the concept of the present application, and these are within the protection scope of the present application. Therefore, the patent protection scope of the present application should be subject to the appended claims.

[0141] Those skilled in the art can understand that the above-described embodiments are specific embodiments for implementing the present application, and in actual applications, various changes can be made in form and details without departing from the spirit and scope of the present application.

Claims

1. A method for evaluating key PVT angles based on a probabilistic integral transform, characterized in that, The method comprises the following steps: simulate N design samples randomly sampled at each PVT corner to obtain a performance index vector, and all the performance index vectors constitute an original data set S; model the performance index vector of each PVT corner by using a kernel density estimation method to obtain a probability density function and a cumulative distribution function of a circuit performance parameter; map the performance index vector to a standard normal distribution variable through a probability integral transformation; construct a multivariate Gaussian distribution model based on the mapped data; obtain a new sample based on the multivariate Gaussian distribution model, calculate the cumulative distribution probability of each new sample at each PVT corner, and map the new sample to an original circuit performance space through an inverse transformation to obtain the original circuit performance of the new sample at the PVT corner; The new sample and the original data set S constitute a complete data set , define the index of the worst PVT angle , count the frequency of each angle in the data set as the worst PVT angle , and sort the key PVT angle set according to the frequency, with the highest frequency being the first key PVT angle.

2. The method of claim 1, wherein, the worst PVT angle is defined as: where n e {1,2,..., N+N new} wherein, represents the circuit performance parameter at the nth sample point and the kth PVT corner, K is the number of PVT corners, k represents a certain PVT corner, and N is the number of samples in the original data set S, is the number of new samples.

3. The method of claim 1, wherein, The probability density function The expression for the probability density function is: where g( ) is a kernel function, represents the bandwidth at the kth PVT corner, y represents the circuit performance parameter, represents the circuit performance parameter at the nth sample point and the kth PVT corner, and N is the number of samples in the original data set S; The cumulative distribution function The expression for the cumulative distribution function is: .

4. The method of claim 3, wherein, The kernel function is one of a Gaussian kernel, an Epanechnikov kernel or a uniform kernel, the The calculation method is as follows: wherein is the absolute median deviation of all performance indicator parameters in the original data set S under the kth PVT angle, and N is the number of samples in the original data set S.

5. The method of claim 3, wherein, the performance index vector is mapped to a standard normal distribution variable through a probability integral transformation, which comprises: calculating a circuit performance parameter for the nth design sample probability of occurrence , wherein, ; mapping the probability to a standard normal distribution space by using an inverse function of a standard normal distribution cumulative distribution function.

6. The method of claim 1, wherein, The multivariate Gaussian distribution model is constructed based on the mapped data, which comprises that the mapped data constitute a K-dimensional vector, denoted as: { N is the number of samples in the original dataset S; The Gaussian distribution model is expressed as: ; wherein is the covariance matrix, denoted as ; I is the identity matrix, denotes the sample covariance matrix, , hyperparameters .

7. The method of claim 6, wherein, The hyperparameter λ is determined through cross-validation, and specifically comprises: sample set Divide into P non-overlapping subsets; divide the subsets, select a single subset as a test set, and the rest as a training set, and there are P divisions; For each split, based on all the sampling points in the training set, compute hyperparameters from the covariance matrix formula covariance; According to the covariance calculation, the likelihood function of each sampling point in the test set under different λ values is calculated, and the sum is summed up on different partitions of the test set, and the maximum likelihood value sum is selected as the optimal value.

8. The method of claim 1, wherein, The method further comprises: Select the first r key PVT angles to construct an index set The remaining key PVT angles form a candidate set. Calculate the candidate set The PVT angle with the highest coverage is selected as the (r+1)th key PVT angle, and the (r+1)th key PVT angle is updated in the index set. In the process, calculate the updated set of indices. The coverage rate, up to the updated index set. Able to cover the sample set The worst PVT angle among all samples .

9. The method of claim 8, wherein, The coverage The formula for the calculation is: wherein, is an indicator function, K is the number of PVT angles, and when , otherwise 0; N is the number of samples in the original dataset S, is the number of new samples; The (r+1)th key PVT angle is determined by: , denotes a certain PVT angle.

10. A key PVT angle evaluation device based on a probability integral transform, characterized by comprise: An original data set S construction module is configured to simulate N design samples randomly sampled at each PVT corner to obtain a performance index vector, and all the performance index vectors constitute an original data set S; A kernel density estimation modeling module is configured to model the performance index vector of each PVT corner by using a kernel density estimation method to obtain a probability density function and a cumulative distribution function of a circuit performance parameter; A mapping module is configured to map the performance index vector to a standard normal distribution variable through a probability integral transformation; A Gaussian distribution model construction module is configured to construct a multivariate Gaussian distribution model based on the mapped data; An inverse transformation module is configured to obtain a new sample based on the multivariate Gaussian distribution model, calculate the cumulative distribution probability of each new sample at each PVT corner, and map the new sample to an original circuit performance space through an inverse transformation to obtain the original circuit performance of the new sample at the PVT corner; a key PVT angle evaluation module, configured to form a complete data set by combining the new sample and the original data set S , define an index of the worst PVT angle , count the frequency of each angle in the data set as the worst PVT angle , and sort the key PVT angle set according to the frequency, wherein the first key PVT angle has the highest frequency. 11.An electronic device comprising a processor, a memory, and a computer program stored on the memory and capable of running on the processor, characterized in that, the processor implements the steps of the key PVT corner evaluation method based on the probability integral transformation according to any one of claims 1-9 when executing the computer program.

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