Research ArticleIdentification of Psychological Crisis Signals of College StudentsBased on the Dufferin Equation

Jianping Zhao 1 and Haitao Song2

1Mental Health Education Center, Xinxiang Vocational and Technical College, Xinxiang, Henan 453000, China2Public Course Teaching Department, Xinxiang Vocational and Technical College, Xinxiang, Henan 453000, China

Correspondence should be addressed to Jianping Zhao; zhaojianping@xxvtc.edu.cn

Received 23 August 2021; Revised 6 September 2021; Accepted 7 September 2021; Published 18 September 2021

Academic Editor: Miaochao Chen

Copyright © 2021 Jianping Zhao and Haitao Song. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original workis properly cited.

This paper presents an in-depth analysis and research on the identification of psychological crisis signals of college students usingthe optimized Dufferin equation. The early warning index system of college students’ psychological crisis was established andtested on 300 junior college students, and the early warning system of college students’ psychological crisis was established byusing structural equation model, focusing on the mediating effect of coping mode between stress source and stress responseand the mediating effect of stress source between social support and stress response. At the same time, the characteristics ofpsychological crises among college students of different genders and grades were compared and analyzed. To address theshortcomings of the classical Dufferin equation with limited noise immunity, the use of a higher-order double-coupledDufferin system was further improved. A detection model based on the higher-order double-coupled system was established,and its feasibility was verified by the psychological crisis signal. The geometric features of the phase trajectory are adopted asthe basis for judging the system state, which greatly reduces the computational effort. Based on defining the conceptualconnotation of college students’ psychological crisis behavior system, the vulnerability of college students’ psychological crisisbehavior system is interpreted from the perspective of system self-organization theory, and the vulnerability of college students’psychological crisis behavior is mainly expressed in latent and manifest states, and its vulnerability transformation is a self-organization process. A questionnaire survey was conducted for ordinary college students to examine the performance ofcollege students’ vulnerability state of the subject who endured college students’ psychological crisis behavior, and it wasconcluded that most college students appear to be normal and healthy on the surface, but college students’ vulnerability is inan uncertain state of intermediate transition.

1. Introduction

A psychological crisis refers to a state of emergency in whicha person is in. When the individual feels overwhelmed by amajor change, the psychological equilibrium will be brokenand the normal physiological life will be disturbed. If theinner tension cannot be eliminated and keeps accumulating,there will be disorientation and even disorder in thinking andbehavior, and the individual will enter a state of imbalance,which will produce a psychological crisis [1]. A psychologicalcrisis occurs when an individual realizes that an event or sit-uation exceeds his or her ability to cope. Among college stu-dents, common psychological imbalances are anorexia,

autism, isolation, violence, running away from home, andeven suicide. Although the number of suicides among thepublic, including college students, has decreased, the situa-tion remains critical. Compared to cancer patients and theterminally ill elderly, college students are not considered ahigh-risk group for the psychological crisis, but they are con-sidered the pillars of society and are one of the groups thatare highly influenced by social concerns [2]. There is confu-sion and even disorder of thinking and behavior and enteringa state of imbalance, which creates a psychological crisis. Theemergence of psychological crisis is because the individualrealizes that a certain event or situation exceeds his abilityto cope. At present, the theoretical research on psychological

HindawiAdvances in Mathematical PhysicsVolume 2021, Article ID 4057328, 12 pageshttps://doi.org/10.1155/2021/4057328

crisis among college students is relatively mature, but thereare fewer studies that establish early warning models andeven fewer studies that involve the analysis of mediatingeffects. In this paper, based on the index system of previousstudies, we establish an early warning model of psychologicalcrisis among college students, apply the effect analysis to thetheoretical study of psychological crisis, study the mediatingeffect of the mediating variables in the hidden variables, andestablish a structural equation model to determine the levelof psychological crisis warning [3]. Although the suicide rateof college students has been reduced in recent years, itsimpact should not be underestimated due to the specialnature of their status. Therefore, it is necessary to intervenein the psychological crisis of college students. In this paper,we establish a structural equation model to identify the psy-chological crisis status of college students and their degrees,to help relevant professionals to take appropriate interven-tion measures.

We systematically study the psychological crisis behaviorof college students from the aspects of characteristic perfor-mance, current situation review, model establishment,mechanism analysis, element identification, and applicationresearch and provide a theoretical basis for the healthy man-agement of college students’ psychological crisis behavior[4]. The study will put forward the vulnerability characteris-tics of college students’ psychological crisis behavior, explainthe process of transforming the vulnerability of college stu-dents’ psychological crisis behavior, establish a theoreticalframework for analyzing the vulnerability of college stu-dents’ psychological crisis behavior, and explore the drivingfactors and mechanisms of college students’ psychologicalcrisis behavior, to understand the internal logic behind theevolution of college students’ psychological crisis behavior,which can enrich the psychological crisis and interventionresearch. It is hoped that the research results can be enrichedby understanding the inner logic behind the evolution of col-lege students’ psychological crisis behaviors and interven-tions, and that the research results can be more theoreticaland academic. Weak signal detection technology is mainlyused to analyze qualitatively and quantitatively the usefulsignals in strong noise background through mathematicaland physical methods, electronic science and technology,information theory, and other methods. The weak signaldetection technology mainly studies the statistical character-istics of the signal to be measured and the background noiseand their differences and uses a series of signal processingmethods to detect the useful signal components from thenoise, which in turn meets the needs of modern scientificresearch and technical applications [5]. At present, weak sig-nal detection technology is widely used in many importantfields such as communication engineering, mechanical engi-neering, medicine, and electromagnetism and has receivedwide attention from scholars in various fields.

However, pure mental health education is not enough tosolve the current psychological crisis problem, and scientifictheories and mature management systems are needed for theprevention and effective resolution of psychological crises.Although the suicide rate of college students has decreased,due to the particularity of their identities, their impact

should not be overlooked. A scientific theory of psychologi-cal crisis management for college students and a mature psy-chological crisis management system for college studentscan effectively protect the safety of students and maintainthe harmony of schools and the stability of society. However,there is a lack of research on the psychological crisis man-agement of college students in China, and the relevant theo-ries have not yet formed a system, and the psychologicalcrisis management system of college students needs to begradually improved. For example, from the perspective ofsystem self-organization theory and psychology, we interpretthe multistate presentation of college students’ crisis vulner-ability and its transformation process; from the perspectiveof behavioral psychology and engineering, we interpret themechanism of college students’ psychological crisis behavior;from the perspective of health management and mentalhealth education, we propose extended thinking on the pre-vention of college students’ psychological crisis behavior andpropose some operational measures on college students’ psy-chological crisis decision-making, intervention system, andhealth education. The study also proposes some operationalmeasures for the decision-making, intervention system, andhealth education of college students.

2. Current Status of Research

The psychological crisis is a state of the psychological imbal-ance that occurs when an individual faces sudden or majorlife adversity (e.g., death of a loved one, marital breakup,or natural or manufactured disasters), which is characterizedby suddenness, urgency, distress, helplessness, and danger,and may lead to suicide or mental breakdown. Manyscholars hold these views on the concept of psychologicalcrisis, and most of the existing literature is based on this con-cept [6]. People have been accustomed to consider psycho-logical crises as catastrophic encounters or negative factors.Nowling and Seeger argued the overemphasis on the hazardsof the emergency event itself, equating psychological crisiswith sudden catastrophic events and responding to themaccording to emergency management [7]. It can enrich psy-chological crisis and intervention research, so that theresearch results have better theoretical and academic nature.The weak signal detection technology mainly uses mathe-matical and physical methods, electronic science technology,information theory, and other methods to qualitatively iden-tify useful signals in the background of strong noise. Bradleyet al. suggested that by informing the person concerned toadopt a reasonable way to deal with the stressful event andusing supportive therapy to help the individual to pass thepsychological crisis and restore his or her normal level ofadaptation, the potential trauma can be avoided or mitigatedto the impact of potential trauma on the client is avoided ormitigated [8]. This definition of the concept based on trau-matic events is biased. Instead, Andersson et al. argue thata crisis no longer means an impending disaster, but a neces-sary turn in the development of life the study of the psycho-logical double should be transformed by stagnating only atthe negative level [9] and the study of subjective experience,positive traits, and positive mechanism interventions for

2 Advances in Mathematical Physics

short-sightedness and individual social functioning recovery[10]. In recent years, positive psychology, which studies sub-jective experience, positive traits, and positive institutions,has emerged abroad and gradually attracted the interestand attention of experts and scholars in the field of psycho-logical crisis research of college students in China, formingan intervention concept that emphasizes the positivity ofindividual growth. Some scholars have shown that 79.7%of college students think that they can get through the psy-chological crisis by their strength [11].

Time-frequency analysis can describe the time-divisionalcharacteristics of the signal according to different time inter-vals, and the steady-state characteristics in the short termand the nonstationary variation trend in the long term canbe well expressed. Since the signal acquisition is affected bythe specific working conditions, the acquired signal is inmany cases a complex nonstationary signal. Bothfrequency-domain analysis and time-domain analysis can-not reflect the nonlinear or nonstationary characteristics ofthe signal, and some features that can only be expressed atspecific nodes may be overwhelmed. The common time-frequency analysis methods include short-time Fouriertransform, wavelet analysis, Wigner-Ville distribution, andS-transform. To address the problem of difficult informationacquisition due to rotational speed fluctuations. Sterelnyobtained more accurate short-time order spectra within thetime-frequency window by cutting from transient frequen-cies and using a fast path optimization algorithm to estimatethe rotational speed transform of nonsmooth signals [12].Resnik et al. concluded that psychological crisis interventionconsists of 3 stages. Firstly, the interventionist should under-stand the causes that lead to the psychological crisis of theintervened person, then develop an intervention strategyaccording to its causes, perform a crisis intervention forthe intervened person according to the coping strategy,and adjust the plan at any time during the interventionaccording to the feedback from the intervened person [13].From the perspective of health management and mentalhealth education, it puts forward extended thinking on pre-venting college students’ psychological crisis behavior andputs forward some practical measures for college students’psychological crisis decision-making, intervention system,and health education. The characteristics of the psychologi-cal crisis intervention method are that it breaks down thepsychological crisis into smaller parts and then intervenes,and it also pays attention to developing and improving thepsychological crisis coping skills and abilities of the inter-vener [14].

Psychological crisis, as a state of intense psychologicalstress, can have a strong impact on the physiological func-tions of the organism and cause great harm. It mainly affectsthe functions of the nervous system, digestive system, andimmune system, which in turn leads to a variety of somaticsymptoms, the most common being somatic pain and sleepdisorders. Therefore, research has focused on how to reduceor even eliminate the adverse effects of psychological crises.Psychological crisis intervention is a technique to provideeffective help and psychological support to individuals in apsychological crisis, to prevent the occurrence of psycholog-

ical crisis by mobilizing their potential to reestablish orreturn to the precrisis psychological equilibrium, and toacquire new skills.

3. Analysis of the Dufferin Equation for theIdentification of Psychological CrisisSignals of College Students

3.1. Improved Dufferin Equation Signal Identification Design.Since the Dufferin equation is well suited to perform detec-tion of weak signals, it is necessary to further investigatethe Dufferin equation. First, the relevant derivation of theDufferin equation is given [15]. It not only has the character-istics of being extremely sensitive to initial conditions, butalso has immunity to Gaussian white noise. The dynamiccharacteristics are very rich, so it has a good simulationeffect for engineering application scenarios. The Dufferinchaotic oscillator is a typical nonlinear system with bothextreme sensitivity to initial conditions and immunity toGaussian white noise, with very rich dynamical properties,and thus has a good simulation for engineering applicationscenarios. In the study of forced vibration systems with non-linear restoring forces, Dufane added a cubic nonlinear termto describe the spring vibration model in mechanical prob-lems and proposed a standardized dynamical equationknown as the Dufane equation.

x::− k x

:−U ′ xð Þ = g tð Þ, ð1Þ

where k is the damping coefficient, U ′ðxÞ is the potentialfunction, and gðtÞ is the periodic function. It has beenproved that there exists a unique solution to the equation,but the solution of the equation does not have an exact ana-lytical formula, and the nonlinear equation can only besolved by simulation through numerical simulation. In thispaper, the fourth-order Longe-Kutta algorithm is used forthe simulation solution, and the nonlinear equation isexpressed by coordinate transformation as follows:

x:: = y,y:: = −ky +U ′ xð Þ − g tð Þ:

(ð2Þ

The process of discretizing the above equation and solv-ing the iterations using the Longe-Kutta algorithm can beexpressed as follows:

Xn = xn−1 −h6 K1 − 2K2 − 2K3: + K4ð Þ, ð3Þ

Yn = yn−1 −h6 L1 − 2L2 − 2L3: + L4ð Þ, ð4Þ

K1 = yn, L1 = −ky +U ′ xð Þ − g tð Þ, ð5Þ

K2 = yn −hL12 , L2 = −kyn +U ′ x + hy1

2

� �− g tð Þ, ð6Þ

3Advances in Mathematical Physics

K3 = yn −hL22 , L2 = −kyn +U ′ x + hy2

2

� �− g tð Þ, ð7Þ

K4 = yn −hL32 , L2 = −kyn +U ′ x + hy3

2

� �− g tð Þ, ð8Þ

where h is the calculation step, i.e., the discrete signaltime interval. Since the Duffing system is sensitive to peri-odic signals with the same frequency as the currents and isimmune to zero-mean Gaussian noise, it is well suited forthe detection of weak signals [16]. The Duffing-Holmes typeequation for weak signal detection is the most developedmethod among many existing studies on nonlinear systems.When the amplitude of the periodic current A is very small,the amplitude of the oscillation of the current is very weak,and the influence on the Dufferin system is also limited.The phase trajectory oscillates periodically around one ofthe two fixed points, and the oscillation period is the drivingforce period T = 2π/ω. At this time, the whole phase trajec-tory can be regarded as the superposition of two kinds ofmotions, and the phase trajectory makes periodic oscillationaround one of the two fixed points, and the oscillationperiod is the current period T = 2π/ω, as shown in Figure 1.

When the amplitude A of the periodic dynamicsincreases slightly, the oscillation region of the phase trajec-tory around the fixed point gradually becomes larger and aperiodic crossover frequency appears when A continues toincrease to the point where the system oscillates back andforth between these singularities to form a complex motiontrajectory, the system enters a chaotic motion state.Although the trajectory of the system is irregular, the regionof motion is finite, so chaotic motion is different from ran-dom motion. From the above analysis of the dynamics ofthe Dufferin system, we can see that the Dufferin system isvery sensitive to the change of parameters, and the phase tra-jectory of the system will change significantly with thechange of the amplitude A of the periodic currents [17].When the driving force amplitude A increases to 0.83, thesystem jumps to a large-scale periodic state. Therefore, asmall change in the periodic driving force A can cause thesystem state to jump. It is important to pay special attentionto the fact that the system trajectory is in chaotic motionwhen the amplitude of the current is A = 0:82, and the sys-tem jumps to the large-scale periodic state when the ampli-tude of the current A increases to 0.83. Therefore, a smallchange in the periodic current A can cause a jump in the sys-tem state. The Dufferin system also makes full use of thisparameter-sensitive property to achieve weak signaldetection.

As the period currents, A increases from 0 to 1, and thetrajectory of the Dufferin system has four states of motion:homogeneous orbit, periodic bifurcation, chaos, and large-scale cycle. The state of the Dufferin system changes fromchaotic to large-scale periodic as the amplitude of the peri-odic current A increases from 0.825 to 0.826. This showsthat the state of the system is sensitive to parameter A, andthere is a critical value of Ad = 0:825 for the amplitude ofthe periodic current A. The response of the system becomesworse, and the chaotic state no longer jumps to the large-

scale cycle. This makes the classical Dufferin system unus-able for most practical engineering signal detection. Toaddress these problems, the classical Dufferin system isimproved by time scale variation.

dxdt

= 1w0

dx τð Þdτ

,

d2x

dt2= −2w2

0

d2x τð Þdτ2

:

8>>><>>>:

ð9Þ

Converting the Dufferin system with a periodic currentfrequency ω = 1 rad/s in Equation (9) into an equation witha time scale τ,

−2w2

0

d2x τð Þdτ2

+ 1w0

dx τð Þdτ

= Ad cos w0τð Þ: ð10Þ

While lifting the frequency limit, the signal to be mea-sured must also satisfy the small-signal condition in termsof amplitude. Studies have shown that when the amplitudeof the signal to be measured is too large, the phase trajectorycharacteristics of the Dufferin system will be destroyed. Thesignal to be measured needs to be scaled up or down beforeinput to the Dufferin system to meet the amplitude detectionrange of the Dufferin system as much as possible. In additionto the need to limit the frequency limit and amplitude of thesignal to be measured, the classical Dufferin system also hasthe problem of initial phase mismatch, and the initial phaseof the actual engineering signal is usually an unknown quan-tity. Consider the extreme case that if the initial phase of thesignal to be measured is opposite to the phase of the periodiccurrents, the periodic currents are partly canceled by the sig-nal to be measured and thus the system state cannot bejumped. If the initial phase of the signal to be measured isopposite to the phase of the periodic driving force, the peri-odic driving force will be partially offset by the signal to bemeasured, causing the system state to fail to jump.

The traditional method is to input the signal directly intothe Dufferin system for recognition, and the effect of directrecognition is not obvious due to the relatively large influ-ence of noise. Therefore, it is thought to first use some sim-ple noise reduction methods to process the signal for noisereduction or filtering using filters and then input theobtained signal into the Dufferin system, which effectivelyreduces the signal-to-noise ratio threshold of the Dufferinsystem for recognizing weak signals, as shown in Figure 2.To improve the detection sensitivity of ultrasonic guidedwaves, an ultrasonic guided wave identification methodbased on the Lyapunov exponent property of the Dufferinequation is proposed, which utilizes the sensitivity of theDufferin equation to the system parameters and its immu-nity property to noise signals. First, the mathematical princi-ple of the Dufferin equation for detecting guided wavesignals is analyzed; second, how to set the parameters ofthe detection system is discussed, and the Dufferin systemthat can be used to detect guided wave signals is given; again,the advantages and disadvantages when using phase

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trajectory diagrams, three-dimensional stereograms, spectralanalysis, and chaos discrimination using Lyapunov expo-nents are compared [18].

The validity and advantage of using the Lyapunov expo-nent for chaos identification are illustrated, and the suitabledetection system is selected by the characteristics of the Lya-punov exponent of the system before and after the inputguided wave signal with the variation of the amplitude ofthe current F. And its displacement-time curve, velocity-

time curve, and displacement and velocity spectrum curveshave all changed significantly. Therefore, the Dufane systemcan be studied through these aspects. Finally, the effective-ness of the method for identifying weak ultrasonic guidedwaves under strong noise is demonstrated by numericallysimulating the different effects of noise and guided wave sig-nal on the Lyapunov exponent. The Lyapunov exponent isone of the quantitative indicators used to describe this phe-nomenon, which characterizes the average exponential rate

0.00.0

0.1

0.1

0.2

0.2

0.3

0.3

0.4

0.4

0.5

0.5

0.6

0.6

0.7

0.7

0.8

0.8

0.9

0.9

1.0

1.0

Noice variance

Phas

e tra

ject

ory

varia

nce

Classic duffing systemHigh-order dual-coupling system

Figure 2: Comparison of noise immunity of double-coupled system and classical system.

3

2

1x

0 100 200 300 400 500

Time (s)

(a)

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Y

0.0 0.5 1.0 1.5 2.0 2.5 3.0

X

(b)

Figure 1: Phase trajectory of the Dufferin system.

5Advances in Mathematical Physics

of convergence or divergence between neighboring orbits ofthe system in phase space over time.

δx1j j = f x0 − δx1j jð Þ + f x0 + δx1j jð Þ2

��������: ð11Þ

Since there is no exact analytical solution for the Duf-ferin system, the magnitude of the curative force will affectthe numerical solution and put the system in different states.In the experiment, it is found that when the Dufferin systemis in a large-scale periodic state, small changes in the peri-odic curative force are also directly reflected in the outputresponse of the system.

Li = limt⟶∞

1tln δx1 xi, tð Þk k

δxi xi, 0ð Þk k : ð12Þ

For nonlinear differential equations, it is generally diffi-cult to obtain exact solutions, but the nature of solutions(e.g., periodicity and stability) can be inferred from the char-acteristics of differential equations, i.e., the use of qualitativetheory and stability theory is an effective means to studynonlinear differential equations. In chaos science, the changeof parameters of a nonlinear system sometimes causes theessential change of the system, and the reaction of thischange to the three-dimensional Dufferin chaotic system isthe interconversion between the chaotic motion states ofthe phase trajectory diagram of the system and the macro-cycle or other motion states, and the sign of the maximumLyapunov exponent is changed, and its displacement-timecurve, velocity-time curve, and the displacement and veloc-ity spectral curves are significantly changed. Therefore, theDufferin system can be investigated in these aspects. Theprinciple of detecting weak signals by the Dufferin systemand the feasibility of using the Dufferin system to detectweak ultrasonic guided waves are explored.

S tð Þ = s tð Þ − σe tð Þ: ð13Þ

Both the single system and the dual-coupled system areadjusted to the critical chaotic state and a sinusoidal signalwith an amplitude of 0.01 is input. The phase trajectory fluc-tuation caused by the noise is characterized by the meansquared difference of the system output before and afterthe noise addition, and the smaller the mean squared differ-ence is, the smaller the effect of the noise on the output,which is defined as follows:

ξ = limN⟶∞

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N + 1〠N

i

xn ið Þ + x0 ið Þ2� �vuut : ð14Þ

In this paper, the geometric features of phase trajectoriesare used as the characteristic quantity to determine the sys-tem state. The geometric features of phase trajectory arecharacteristic parameters to measure the shape of phase tra-jectory images, which can reflect the difference between dif-ferent shapes of phase trajectory [19]. The system suffers

from a kind of deviation or disturbance that needs to beovercome. Some individuals with high vulnerability andlow frustration resistance, if the self-organizing defensemechanism cannot be effectively used and cannot achieveharmony and unity, will inevitably present a kind of imbal-ance and instability. As the currents increase, the systemchanges from chaotic to large-scale periodic state, and thephase trajectories change from chaotic to regular spirals,and the geometric features show a significant increase ordecrease before and after the system state jump. After enter-ing the large-scale cycle, the wrap-around area of the phasetrajectory spiral expands slightly with the increase of the cur-rents, and the geometric features can also show the relativechange with the currents.

x0 =1

M∬Dsds

: ð15Þ

Since the phase trajectories are scattered by the fourth-order Longe-Kutta method, the cumulative summation isused instead of the integral operation. If the value of a pixelpoint is 1, the corresponding area is also 1. To enhance thegeneralizability of the polar radius invariant moments, thefeatures are normalized and the final polar radius invariantmoments and polar radius central moments are discretized.

3.2. Experimental Analysis of Students’ Psychological CrisisSignal Recognition. Vulnerability is an inherent property ofany system itself. It has been shown that individuals withhigh vulnerability are prone to negative developmental evo-lutionary outcomes, while individuals with low vulnerabilityare prone to positive developmental evolutionary outcomes[20]. It is manifested when the system suffers a perturbationand is unable to cope with it, prompting the system tochange its structure and function in a state of instability.The psychological crisis behavior system of college studentsincludes various behaviors including suicide, injury, andpsychological crisis, which are behaviors taken under thestate of psychological behavior instability and can hardlybear the crisis. Thus, the vulnerability of the psychologicalcrisis behavior system of college students is a complex ofthe results of trait processes. The human psychologicalbehavior is a dynamic homeostatic development system, akind of conscious self-organized functional system. Theself-organization process is a complex adaptive system with-out external intervention or perturbation, and the systemwill spontaneously evolve from disorder to order, fromlow-level order to high-level order. From the perspective ofsystem self-organization, college students who have psycho-logical crisis behaviors often show that their “self-organization” dynamics cannot be effectively exercised, andthey are in a highly vulnerable state of manifestation.

In general, the system suffers from a deviation or pertur-bation to be overcome, and some individuals with low vul-nerability tolerance, if the self-organized defensemechanism cannot be effectively used to achieve harmonyand unity, will inevitably present an imbalanced and unsta-ble psychological state. In this equilibrium process, vulnera-bility plays a negative role, manifested as a state of

6 Advances in Mathematical Physics

vulnerability manifestation. From the system’s developmentand evolution, due to various risks and pressure sources ofperturbation, highly vulnerable individuals will enter adestabilized crisis state, and when the psychological systemdramatic changes caused by the psychological shock willmake the original steady state no longer exist, the initialinternal stability of the orderly variables will lose its domi-nant position, and the system will appear in the sharp riseand fall; once there is a constantly amplified giant rise andfall across the system barrier, the long-range coherence andsweep occur, because in the process of cognition of changesand risks, subjects who endure different crises will have dif-ferent cognitive strategies. These involve various economic,social, and behavioral scientific theories. At this stage, wemust consider the uncertainty of the psychological systemand the impact of information. The whole system, over time,when the system rises and fall beyond the psychologicalthreshold, the system will mutate into a psychological crisisbehavior problem.

With the increasing richness of the concept of vulnera-bility and the broadening of its application fields, the theo-retical model of vulnerability has undergone the process ofshifting from single to multiple perturbations, from the vul-nerability of natural systems to the coupling of nature andsociety, and from the static analysis of vulnerability to thedynamic analysis of the vulnerability, and numerous analyt-ical frameworks have emerged to explore the causes of vul-nerability and the interactions of its drivers from differentperspectives. The theoretical model of mature system vul-nerability that is more recognized by the academic commu-nity is shown in Figure 3.

Regardless of the theoretical models of vulnerability,they are all conceptual representations of the causes andmechanisms of vulnerability, and each conceptual modelattempts to reveal the essence of vulnerability and explorethe intrinsic linkages and complex roles between the charac-teristic elements of vulnerability and their drivers from dif-

ferent perspectives. It can be seen that the internalcharacteristics of the system are the main and direct factorsof vulnerability generation, while the interaction betweendisturbances, stresses, and the system to reduce or amplifyits vulnerability is the driver of vulnerability evolution, butthis driver is through the influence of the internal character-istics of the system to make changes in vulnerability and ulti-mately through the system’s sensitivity to disturbances andits ability to cope, resilience to manifest.

Combined with the latest development trend of vulnera-bility research, the construction of the vulnerability theoret-ical model of college students’ psychological crisis behaviorneeds to pay attention to two requirements: first, the prob-lem of multiple spatial and temporal scales. We should payattention to different groups of college students in differentregions, portray the vulnerability in different spaces, andemphasize the evolution of vulnerability over time; the sec-ond is the problem of multiple crises [21]. Colleges and uni-versities are no longer “ivory towers”, and college studentsare usually exposed to multiple perturbations at multiplescales and interactions with each other, and this understand-ing has formed a consensus in many studies. Therefore, it isthe future development direction to build a vulnerabilitytheory model of multiple crisis perturbations. As vulnerabil-ity research has penetrated various disciplines, innovativetechnology has broadened the perspective of vulnerabilityresearch, and exploring the characteristic elements of vul-nerability from complex dynamic systems has become a tire-lessly pursued goal in academia. It shows that there is a largepeak at the center frequency of 70 khz. Furthermore, theecho signals under the five working conditions are subjectedto spectrum analysis, the ratio of the peak amplitude of thedefect echo after spectrum analysis to the peak value of theincident wave after spectrum analysis is defined as the reflec-tion coefficient, and the correction coefficient k is selected as0.8. As the core subject of human own vulnerability research,psychological factors have complexity, uncertainty, and are

Campus risk

Academic risk

Social risk

Moral Hazard

Employment risk

Cyber risk

Health difference

Source difference

Grade difference

Poverty gap

Family differences

College studentsensitivity

Cognitive balance Emotion regulation

Quality of will Behavior control

Seek support Personality Traits

Coercive driving effect, structural driving effect, cumulative driving effect

Vulnerability

Figure 3: Model diagram of twine.

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difficult to measure. This is because in the process of cogni-tion of change and risk, subjects who endure crisis differ-ently will have different cognitive strategies, and theseinvolve various economic, social, and behavioral science the-ories, and at this stage, the uncertainty of the psychologicalsystem and the incompleteness of information should beconsidered.

The conceptual model is mainly proposed for the non-structural analysis of the vulnerability, which is difficult tostructure due to the multiplicity of system elements in thisstudy and the complexity of their coupling effects, and themultiplicity of external risks or disturbances. Traditionalvulnerability analysis tends to take a structured quantitativecarrier sensitivity and exposure to measure vulnerability,tending to narrowly describe the ability of the system to losestructure and function. Cumulative vulnerability drive refersto the idea that individuals become more resilient when cop-ing with adversity that is both challenging and not insur-mountable, and that successful coping increases theindividual’s confidence in resisting adversity and, as a result,gains more psychological protective factors. For example, afirst-year student who enters the group life of school adaptsto self-care through military training, and a college studentwho is not familiar with the world becomes mature andcompetent through summer social practice. Moderate riskand stress help individuals to improve their resilience. Chil-dren do not gain interpersonal coping skills when they donot experience family conflict or when they experience mildconflict; children tend to acquire learned helplessness infamilies that are contentious and severe, and moderate con-flict provides children with opportunities for interpersonalcoping skills. Low or high levels of resilience are not likelyto lead to cumulative vulnerability, while moderate levelsof resilience are conducive to more protective factors andenhance individual psychological immunity.

4. Analysis of Results

4.1. Improved Signal Identification Results for the DufferinEquation. Considering the above definition, the amplitudeof the five conditions on the frequency domain expressedin Equations (14) and ((15)), as shown in Figure 4, is thespectral analysis graph of two different working conditions.As can be seen from the figure, because the defect of condi-tion two is relatively small, the amplitude obtained after thespectrum analysis is relatively small, almost no obvious peakand cannot determine whether there is a defect echo. As thedefect is relatively large, the echo is more obvious, and thespectrum can also be seen to contain the center frequencyof 70 khz of the guided wave signal, as shown in the centerfrequency of 70 khz where there is a large peak. Further,the echo signals under the five working conditions are ana-lyzed by spectrum, and the ratio of the peak amplitude ofthe defective echo after spectrum analysis to the peak ofthe incident wave after spectrum analysis is defined as thereflection coefficient, and the correction coefficient k ischosen as 0.8.

The reflection coefficient is plotted with the percentagereduction of the cross-section and compared with the tradi-

tional time-domain definition of the cross-sectional reflec-tion coefficient, as shown in Figure 4, from which it can beseen that the experimental results are uniformly distributedaround the theoretical results, and the reflection coefficientshows a monotonically increasing trend with the increaseof the cross-sectional area, i.e., the larger the defect, thelarger the amplitude and the larger the reflection coefficient.When the defect is relatively small, the amplitude is notobvious. Visualization technology is mature and plays agreat role in the fields of medicine, geological prospecting,geographic information, meteorology, and other fields. Theuse of the method has obvious advantages for the detectionof small defects where the defect echoes cannot be observed,which can be judged directly by observing the change in theLyapunov exponent caused by the echo signal, while the useof the method represented in Figure 4 is not sensitive tosmall defects. The comparison illustrates that the proposedmethod is effective and advantageous. Visualization technol-ogy refers to the theory, method, and technology of exchang-ing data into graphics or images for display and interactiveprocessing using computer graphics and image processingtechniques. It involves various fields such as computergraphics, image processing, computer-aided design, com-puter vision, and human-computer interaction technology.Visualization technology is mature and plays a great rolein the fields of medicine, geological exploration and geo-graphic information, meteorology, etc.

When using the Dufferin system for ultrasonic guidedwave inspection, different procedures need to be operatedand professional engineers and technicians must be availableto determine the presence and extent of damage to the struc-ture. Therefore, it is important to develop a more concise,intuitive, and visual presentation method to reveal the exis-tence of pipeline defects. The Dufferin detection system forultrasonic guided wave signals developed in this paper is acombination of the system’s phase trajectory diagram, Lya-punov index, time-domain analysis, and frequency domainanalysis together. It can be easily done by operating only afew buttons, which is very intuitive and has strong practical-ity. The visualization system is divided into three parts: thechange of the system itself with the characteristics of theamplitude of the current when no signal is added, as shownin Figure 5, and the analog signal or the actual measurementdata is imported into the system, which can be completed bythe button to discriminate the state of its system, includingdiscriminating phase trajectory diagram, Lyapunov index,three-dimensional diagram, frequency domain analysis,and time-domain analysis.

The Lyapunov exponent is used as an indicator for quan-titative analysis of chaotic systems and as an identificationindicator representing defective echo signals. A suitabledetection system was selected according to the change ofthe Lyapunov exponent before and after the input guidedwave signal. The pure noise signal with different noise levelsand the guided wave signal mixed with different noise levelsare input to the detection system, and the Dufferin equationphase trajectory diagram and Lyapunov exponent input aredistinctly different, based on which the ultrasonic guidedwave signal identification is performed. Numerical examples

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show that the method has high sensitivity and can effectivelyidentify the guided wave signals even at a 100% noise level.

4.2. Experimental Results of Psychological CrisisIdentification for Higher Education Students. In this part,we compare and analyze the psychological stress reactionsof higher vocational students and demographic factor indi-cators, find out the significant differences in the demo-graphic factor indicators as the demographic factor

indicators in the early warning indicators, and find out thedifferences in the stress reactions of different backgrounddata by independent sample t-test and ANOVA to providea reference for the establishment of the early warning indica-tor system of psychological crisis. The gender difference inpsychological stress response among college students inhigher education institutions was not significant, but thedata showed that in general, female students have strongerpsychological stress responses than male students. This

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Figure 4: Spectrum analysis under two working conditions.

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may be related to the different physiological conditions, fam-ily upbringing, living environment, and social experiences ofmen and women. Most boys in their student years are lively,adventurous, cheerful, and happy to communicate with theirschool friends in all matters, so they score lower in psycho-logical stress. However, very often, immature bravery oftenmeans impulsiveness, so boys are slightly more intense thangirls in terms of behavioral reactions. Girls are more delicateand quieter when they are students, and they do not like tomake noise, so girls will be weaker than boys in terms ofphysiological stress and behavioral stress reactions. How-ever, delicate feelings tend to be emotional, and girls tendto be sentimental when they encounter problems, so girlsare stronger in terms of psychological stress reactions, asshown in Figure 6.

The difference in psychological stress response amongcollege students in higher education institutions in termsof ethnicity is not obvious, and according to the data, thepsychological stress response of minority college studentsis slightly stronger than that of Han college students. Ethnicminority college students scored lower than Han college stu-dents in three aspects: physiological reaction, psychologicalreaction, and behavioral reaction. This may be related tothe source of minority students, and most of them comefrom remote provinces, far from home, and can only meetwith their family and friends back home during long holi-days, so they cannot get timely support from their familyand friends when they encounter difficulties. Most ethnicminorities have their national languages and scripts, whichare the crystallization of their national wisdom, but they alsobring some communication problems. Especially in knowl-edge learning, most of the knowledge needs to be acquiredwith the help of Chinese and English, and minority collegestudents who have weak proficiency in these two languages

may have difficulties in learning. Therefore, the psychologi-cal stress reflection of minority college students is relativelystronger, as shown in Figure 7.

Figure 7 of the mountain structural model shows thatcoping style is a mediating variable between stress sourceand stress response, and coping style is a mediating variablebetween social support and stress response. According to thedefinition of mediating effect, the mediating effect of copingmode can be measured by the product of the path coefficientfrom stress source to coping mode multiplied by the pathcoefficient from coping mode to stress response, and themediating effect of coping mode is partially mediated at thistime, as can be seen from the calculated results of the estab-lished model in Figure 7. The path coefficient from thestressor to the copying mode is 0.61, and the path coefficientfrom the coping mode to the stress response is 0.48, so themediating effect of the coping mode on the stressor andthe stress response is their product 0.29. The direct effectfrom the stressor to the stress response (i.e., the path coeffi-cient from the social support to the stress response) is 0.52,so the total effect from the stressor to the stress response is0.81. Similarly, the coping style to social support to stressresponse mediating effect can be calculated, which is also apartial mediating effect. The path coefficient of our socialsupport to coping style is 0.78, and the path coefficient ofour coping style to the stress response is 0.48, so the mediat-ing effect of coping style on social support and stressresponse is 0.37. And the direct effect of social support onstress response is 0.47, so the total effect of social supporton stress response is 0.84.

The path coefficient from the stressor to the coping styleis 0.61, and the path coefficient from the coping style to thestress response is 0.48, so the mediating effect of the copingstyle on the stressor and the stress response is 0.29. In

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Figure 6: Comparison of college students in higher education institutions in terms of the psychological stress response.

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summary, the coping style mediates both the source of stressand the stress response and the social support and the stressresponse, and the source of stress mediates the social sup-port and the stress response, and they are both partial medi-ators, which is consistent with our hypothesis, and theconstructed model is reasonable. It indicates that improvingsocial support for individuals can reduce their sources of thecrisis and thus can play a good intervention role in their psy-chological crisis. Cultivating a mature way of coping with acrisis can enable individuals to face the crisis with ease anddeal with it properly. Therefore, when intervening in thepsychological crisis of college students, we should not onlyintervene in the source of stress but also focus on cultivatingtheir mature ways of coping with crisis and improving socialsupport, which is more conducive to the psychologicalhealthy growth of college students.

5. Conclusion

Using the improved Dufferin equation algorithm, theobtained early warning elements of psychological crisisbehaviors are more accurate and effective. The complexityand dynamics of college students’ psychological crisis behav-iors and the limited perception of them make the crisis pre-vention and control face information uncertainty and dataincompleteness, and the traditional quantitative technicalmethods can no longer adapt to the requirements of realisticprevention and intervention. The rough set decision analysismethod based on restricted dominance relationship can

effectively analyze and process various incomplete prefer-ence information, obtain the key elements of psychologicalcrisis behavior early warning from it, objectively identifythe psychological crisis behavior driving factors, and dis-cover the hidden root causes of crisis from it. By construct-ing the early warning element system of college students’psychological crisis behaviors, with the help of the roughset method of double restricted dominance relationship,information processing and data analysis of 300 students’mental health profile information of the university were con-ducted, and a comprehensive discussion was conducted withthe element analysis, effect identification, and crisis transfor-mation to derive the individual differences of college stu-dents’ psychological crisis behavioral vulnerability, whichtruly presents the multiplicity of college students’ psycholog-ical crisis behavioral driving elements and the diversity ofoccurrence mechanisms.

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper.

GFI

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Figure 7: Comparison of fit indices of different models.

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